Internal Rate of Return

Description

Calculates internal rate of return for a series of cash flows, and provides a time diagram of the cash flows.

Usage

IRR(cf0,cf,times,plot=FALSE)

Arguments

Details

cf0=\sum_{k=1}^n\frac{cf_k}{(1+irr)^{times_k}}

Value

The internal rate of return.

Note

Periods in t must be positive integers.

Uses polyroot function to solve equation given by series of cash flows, meaning that in the case of having a negative IRR, multiple answers may be returned.

Author(s)

Kameron Penn and Jack Schmidt

See Also

NPV

Examples

IRR(cf0=1,cf=c(1,2,1),times=c(1,3,4))

IRR(cf0=100,cf=c(1,1,30,40,50,1),times=c(1,1,3,4,5,6))

Net Present Value

Description

Calculates the net present value for a series of cash flows, and provides a time diagram of the cash flows.

Usage

NPV(cf0,cf,times,i,plot=FALSE)

Arguments

Details

NPV=cf0-\sum_{k=1}^n\frac{cf_k}{(1+i)^{times_k}}

Value

The NPV.

Note

The periods in t must be positive integers.

The lengths of cf and t must be equal.

See Also

IRR

Examples

NPV(cf0=100,cf=c(50,40),times=c(3,5),i=.01)

NPV(cf0=100,cf=50,times=3,i=.05)

NPV(cf0=100,cf=c(50,60,10,20),times=c(1,5,9,9),i=.045)

Time Value of Money

Description

Solves for the present value, future value, time, or the interest rate for the accumulation of money earning compound interest. It can also plot the time value for each period.

Usage

TVM(pv=NA,fv=NA,n=NA,i=NA,ic=1,plot=FALSE)

Arguments

Details

j=(1+\frac{i}{ic})^{ic}-1

fv=pv*(1+j)^n

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

Exactly one of pv, fv, n, or i must be NA (unknown).

See Also

cf.analysis

Examples

TVM(pv=10,fv=20,i=.05,ic=2,plot=TRUE)

TVM(pv=50,n=5,i=.04,plot=TRUE)

Amortization Period

Description

Solves for either the number of payments, the payment amount, or the amount of a loan. The payment amount, interest paid, principal paid, and balance of the loan are given for a specified period.

Usage

amort.period(Loan=NA,n=NA,pmt=NA,i,ic=1,pf=1,t=1)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Loan=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}

Balance at the end of period t: B_t=pmt*{a_{\left. {\overline {\, n-t \,}}\! \right |j}}

Interest paid at the end of period t: i_t=B_{t-1}*j

Principal paid at the end of period t: p_t=pmt-i_t

Value

Returns a matrix of input variables, calculated unknown variables, and amortization figures for the given period.

Note

Assumes that payments are made at the end of each period.

One of n, pmt, or Loan must be NA (unknown).

If pmt is less than the amount of interest accumulated in the first period, then the function will stop because the loan will never be paid off due to the payments being too small.

If the pmt is greater than the loan amount plus interest accumulated in the first period, then the function will stop because one payment will pay off the loan.

t cannot be greater than n.

Author(s)

Kameron Penn and Jack Schmidt

See Also

amort.table

Examples

amort.period(Loan=100,n=5,i=.01,t=3)

amort.period(n=5,pmt=30,i=.01,t=3,pf=12)

amort.period(Loan=100,pmt=24,ic=1,i=.01,t=3)

Amortization Table

Description

Produces an amortization table for paying off a loan while also solving for either the number of payments, loan amount, or the payment amount. In the amortization table the payment amount, interest paid, principal paid, and balance of the loan are given for each period. If n ends up not being a whole number, outputs for the balloon payment, drop payment and last regular payment are provided. The total interest paid, and total amount paid is also given. It can also plot the percentage of each payment toward interest vs. period.

Usage

amort.table(Loan=NA,n=NA,pmt=NA,i,ic=1,pf=1,plot=FALSE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Loan=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}

Balance at the end of period t: B_t=pmt*{a_{\left. {\overline {\, n-t \,}}\! \right |j}}

Interest paid at the end of period t: i_t=B_{t-1}*j

Principal paid at the end of period t: p_t=pmt-i_t

Total Paid=pmt*n

Total Interest Paid=pmt*n-Loan

If n=n^*+k where n^* is an integer and 0<k<1:

Last regular payment (at period n^*) =pmt*{s_{\left. {\overline {\, k \,}}\! \right |j}}

Drop payment (at period n^*+1) =Loan*(1+j)^{n^*+1}-pmt*{s_{\left. {\overline {\, n^* \,}}\! \right |j}}

Balloon payment (at period n^*) =Loan*(1+j)^{n^*}-pmt*{s_{\left. {\overline {\, n^* \,}}\! \right |j}}+pmt

Value

A list of two components.

Note

Assumes that payments are made at the end of each period.

One of n, Loan, or pmt must be NA (unknown).

If pmt is less than the amount of interest accumulated in the first period, then the function will stop because the loan will never be paid off due to the payments being too small.

If pmt is greater than the loan amount plus interest accumulated in the first period, then the function will stop because one payment will pay off the loan.

Author(s)

Kameron Penn and Jack Schmidt

See Also

amort.period

annuity.level

Examples

amort.table(Loan=1000,n=2,i=.005,ic=1,pf=1)

amort.table(Loan=100,pmt=40,i=.02,ic=2,pf=2,plot=FALSE)

amort.table(Loan=NA,pmt=102.77,n=10,i=.005,plot=TRUE)

Arithmetic Annuity

Description

Solves for the present value, future value, number of payments/periods, amount of the first payment, the payment increment amount per period, and/or the interest rate for an arithmetically growing annuity. It can also plot a time diagram of the payments.

Usage

annuity.arith(pv=NA,fv=NA,n=NA,p=NA,q=NA,i=NA,ic=1,pf=1,imm=TRUE,plot=FALSE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

fv=pv*(1+j)^n

Annuity Immediate:

pv=p*{a_{\left. {\overline {\, n \,}}\! \right |j}}+q* \frac{{a_{\left. {\overline {\, n \,}}\! \right |j}}-n*(1+j)^{-n}}{j}

Annuity Due:

pv=(p*{a_{\left. {\overline {\, n \,}}\! \right |j}}+q* \frac{{a_{\left. {\overline {\, n \,}}\! \right |j}}-n*(1+j)^{-n}}{j})*(1+i)

Value

Returns a matrix of the input variables, and calculated unknown variables.

Note

At least one of pv, fv, n, p, q, or i must be NA (unknown).

pv and fv cannot both be specified, at least one must be NA (unknown).

Author(s)

Kameron Penn and Jack Schmidt

See Also

annuity.geo

annuity.level

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.arith(pv=NA,fv=NA,n=20,p=100,q=4,i=.03,ic=1,pf=2,imm=TRUE)

annuity.arith(pv=NA,fv=3000,n=20,p=100,q=NA,i=.05,ic=3,pf=2,imm=FALSE)

Geometric Annuity

Description

Solves for the present value, future value, number of payments/periods, amount of the first payment, the payment growth rate, and/or the interest rate for a geometrically growing annuity. It can also plot a time diagram of the payments.

Usage

annuity.geo(pv=NA,fv=NA,n=NA,p=NA,k=NA,i=NA,ic=1,pf=1,imm=TRUE,plot=FALSE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

fv=pv*(1+j)^n

Annuity Immediate:

j != k: pv=p*\frac{1-(\frac{1+k}{1+j})^n}{j-k}

j = k: pv=p*\frac{n}{1+j}

Annuity Due:

j != k: pv=p*\frac{1-(\frac{1+k}{1+j})^n}{j-k}*(1+j)

j = k: pv=p*n

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

At least one of pv, fv, n, pmt, k, or i must be NA (unknown).

pv and fv cannot both be specified, at least one must be NA (unknown).

See Also

annuity.arith

annuity.level

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.geo(pv=NA,fv=100,n=10,p=9,k=.02,i=NA,ic=2,pf=.5,plot=TRUE)

annuity.geo(pv=NA,fv=128,n=5,p=NA,k=.04,i=.03,pf=2)

Level Annuity

Description

Solves for the present value, future value, number of payments/periods, interest rate, and/or the amount of the payments for a level annuity. It can also plot a time diagram of the payments.

Usage

annuity.level(pv=NA,fv=NA,n=NA,pmt=NA,i=NA,ic=1,pf=1,imm=TRUE,plot=FALSE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Annuity Immediate:

pv=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*\frac{1-(1+j)^{-n}}{j}

fv=pmt*{s_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)^n

Annuity Due:

pv=pmt*{\ddot {a}_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)

fv=pmt*{\ddot {s}_{\left. {\overline {\, n \,}}\! \right |j}}=pmt*{a_{\left. {\overline {\, n \,}}\! \right |j}}*(1+j)^{n+1}

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

At least one of pv, fv, n, pmt, or i must be NA (unknown).

pv and fv cannot both be specified, at least one must be NA (unknown).

See Also

annuity.arith

annuity.geo

perpetuity.arith

perpetuity.geo

perpetuity.level

Examples

annuity.level(pv=NA,fv=101.85,n=10,pmt=8,i=NA,ic=1,pf=1,imm=TRUE)

annuity.level(pv=80,fv=NA,n=15,pf=2,pmt=NA,i=.01,imm=FALSE)

Bear Call Spread

Description

Gives a table and graphical representation of the payoff and profit of a bear call spread for a range of future stock prices.

Usage

bear.call(S,K1,K2,r,t,price1,price2,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<K2: payoff =K1-S_t

For S_t>=K2: payoff =K1-K2

payoff = profit + (price1 - price2)*e^{r*t}

Value

A list of two components.

Note

K1 must be less than S, and K2 must be greater than S.

Author(s)

Kameron Penn and Jack Schmidt

See Also

bear.call.bls

bull.call

option.call

Examples

bear.call(S=100,K1=70,K2=130,r=.03,t=1,price1=20,price2=10,plot=TRUE)

Bear Call Spread - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a bear call spread for a range of future stock prices. Uses the Black Scholes equation for the call prices.

Usage

bear.call.bls(S,K1,K2,r,t,sd,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<K2: payoff =K1-S_t

For S_t>=K2: payoff =K1-K2

payoff = profit+(price_{K1}-price_{K2})*e^{r*t}

Value

A list of two components.

Note

K1 must be less than S, and K2 must be greater than S.

Author(s)

Kameron Penn and Jack Schmidt

See Also

bear.call

bull.call.bls

option.call

Examples

bear.call.bls(S=100,K1=70,K2=130,r=.03,t=1,sd=.2)

Black Scholes First-order Greeks

Description

Gives the price and first order greeks for call and put options in the Black Scholes equation.

Usage

bls.order1(S,K,r,t,sd,D=0)

Arguments

Value

A matrix of the calculated greeks and prices for call and put options.

Note

Cannot have any inputs as vectors.

t cannot be negative.

Either both or neither of S and K must be negative.

Author(s)

Kameron Penn and Jack Schmidt

See Also

option.put

option.call

Examples

x <- bls.order1(S=100, K=110, r=.05, t=1, sd=.1, D=0)
ThetaPut <- x["Theta","Put"]
DeltaCall <- x[2,1]

Bond Analysis

Description

Solves for the price, premium/discount, and Durations and Convexities (in terms of periods). At a specified period (t), it solves for the full and clean prices, and the write up/down amount. Also has the option to plot the convexity of the bond.

Usage

bond(f,r,c,n,i,ic=1,cf=1,t=NA,plot=FALSE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{cf}}-1

coupon =\frac{f*r}{cf} (per period)

price = coupon*{a_{\left. {\overline {\, n \,}}\! \right |j}}+c*(1+j)^{-n}

MAC D=\frac{\sum_{k=1}^n k*(1+j)^{-k}*coupon+n*(1+j)^{-n}*c}{price}

MOD D=\frac{\sum_{k=1}^n k*(1+j)^{-(k+1)}*coupon+n*(1+j)^{-(n+1)}*c}{price}

MAC C=\frac{\sum_{k=1}^n k^2*(1+j)^{-k}*coupon+n^2*(1+j)^{-n}*c}{price}

MOD C=\frac{\sum_{k=1}^n k*(k+1)*(1+j)^{-(k+2)}*coupon+n*(n+1)*(1+j)^{-(n+2)}*c}{price}

Price (for period t):

If t is an integer: price =coupon*{a_{\left. {\overline {\, n-t \,}}\! \right |j}}+c*(1+j)^{-(n-t)}

If t is not an integer then t=t^*+k where t^* is an integer and 0<k<1:

full price =( coupon*{a_{\left. {\overline {\, n-t^* \,}}\! \right |j}}+c*(1+j)^{-(n-t^*)})*(1+j)^k

clean price = full price-k*coupon

If price > c :

premium = price-c

Write-down amount (for period t) =(coupon-c*j)*(1+j)^{-(n-t+1)}

If price < c :

discount =c-price

Write-up amount (for period t) =(c*j-coupon)*(1+j)^{-(n-t+1)}

Value

A matrix of all of the bond details and calculated variables.

Note

t must be less than n.

To make the duration in terms of years, divide it by cf.

To make the convexity in terms of years, divide it by cf^2.

Examples

bond(f=100,r=.04,c=100,n=20,i=.04,ic=1,cf=1,t=1)

bond(f=100,r=.05,c=110,n=10,i=.06,ic=1,cf=2,t=5)

Bull Call Spread

Description

Gives a table and graphical representation of the payoff and profit of a bull call spread for a range of future stock prices.

Usage

bull.call(S,K1,K2,r,t,price1,price2,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<K2: payoff =S_t-K1

For S_t>=K2: payoff =K2-K1

profit = payoff + (price2 - price1)*e^{r*t}

Value

A list of two components.

Note

K1 must be less than S, and K2 must be greater than S.

See Also

bull.call.bls

bear.call

option.call

Examples

bull.call(S=115,K1=100,K2=145,r=.03,t=1,price1=20,price2=10,plot=TRUE)

Bull Call Spread - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a bull call spread for a range of future stock prices. Uses the Black Scholes equation for the call prices.

Usage

bull.call.bls(S,K1,K2,r,t,sd,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<K2: payoff =S_t-K1

For S_t>=K2: payoff =K2-K1

profit = payoff+(price_{K2}-price_{K1})*e^{r*t}

Value

A list of two components.

Note

K1 must be less than S, and K2 must be greater than S.

See Also

bear.call

option.call

Examples

bull.call.bls(S=115,K1=100,K2=145,r=.03,t=1,sd=.2)

Butterfly Spread

Description

Gives a table and graphical representation of the payoff and profit of a long butterfly spread for a range of future stock prices.

Usage

butterfly.spread(S,K1,K2=S,K3,r,t,price1,price2,price3,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<=K2: payoff =S_t-K1

For K2<S_t<K3: payoff =2*K2-K1-S_t

For S_t>=K3: payoff =0

profit = payoff+(2*price2 - price1 - price3)*e^{r*t}

Value

A list of two components.

Note

K2 must be equal to S.

K3 and K1 must both be equidistant to K2 and S.

K1 < K2 < K3 must be true.

See Also

butterfly.spread.bls

option.call

Examples

butterfly.spread(S=100,K1=75,K2=100,K3=125,r=.03,t=1,price1=25,price2=10,price3=5)

Butterfly Spread - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a long butterfly spread for a range of future stock prices. Uses the Black Scholes equation for the call prices.

Usage

butterfly.spread.bls(S,K1,K2=S,K3,r,t,sd,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =0

For K1<S_t<=K2: payoff =S_t-K1

For K2<S_t<K3: payoff =2*K2-K1-S_t

For S_t>=K3: payoff =0

profit = payoff+(2*price_{K2}-price_{K1}-price_{K3})*e^{r*t}

Value

A list of two components.

Note

K2 must be equal to S.

K3 and K1 must both be equidistant to K2 and S.

K1 < K2 < K3 must be true.

See Also

butterfly.spread

option.call

Examples

butterfly.spread.bls(S=100,K1=75,K2=100,K3=125,r=.03,t=1,sd=.2)

Cash Flow Analysis

Description

Calculates the present value, macaulay duration and convexity, and modified duration and convexity for given cash flows. It also plots the convexity and time diagram of the cash flows.

Usage

cf.analysis(cf,times,i,plot=FALSE,time.d=FALSE)

Arguments

Details

pv=\sum_{k=1}^n\frac{cf_k}{(1+i)^{times_k}}

MAC D=\frac{\sum_{k=1}^n times_k*(1+i)^{-times_k}*cf_k}{pv}

MOD D=\frac{\sum_{k=1}^n times_k*(1+i)^{-(times_k+1)}*cf_k}{pv}

MAC C=\frac{\sum_{k=1}^n {times_k}^2*(1+i)^{-times_k}*cf_k}{pv}

MOD C=\frac{\sum_{k=1}^n times_k*(times_k+1)*(1+i)^{-(times_k+2)}*cf_k}{pv}

Value

A matrix of all of the calculated values.

Note

The periods in t must be positive integers.

See Also

TVM

Examples

cf.analysis(cf=c(1,1,101),times=c(1,2,3),i=.04,time.d=TRUE)

cf.analysis(cf=c(5,1,5,45,5),times=c(5,4,6,7,5),i=.06,plot=TRUE)

Collar Strategy

Description

Gives a table and graphical representation of the payoff and profit of a collar strategy for a range of future stock prices.

Usage

collar(S,K1,K2,r,t,price1,price2,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =K1-S_t

For K1<S_t<K2: payoff =0

For S_t>=K2: payoff =K2-S_t

profit = payoff + (price2 - price1)*e^{r*t}

Value

A list of two components.

See Also

collar.bls

option.put

option.call

Examples

collar(S=100,K1=90,K2=110,r=.05,t=1,price1=5,price2=15,plot=TRUE)

Collar Strategy - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a collar strategy for a range of future stock prices. Uses the Black Scholes equation for the call and put prices.

Usage

collar.bls(S,K1,K2,r,t,sd,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =K1-S_t

For K1<S_t<K2: payoff =0

For S_t>=K2: payoff =K2-S_t

profit = payoff+(price_{K2}-price_{K1})*e^{r*t}

Value

A list of two components.

See Also

option.put

option.call

Examples

collar.bls(S=100,K1=90,K2=110,r=.05,t=1,sd=.2)

Covered Call

Description

Gives a table and graphical representation of the payoff and profit of a covered call strategy for a range of future stock prices.

Usage

covered.call(S,K,r,t,sd,price=NA,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K: payoff =S_t

For S_t>K: payoff =K

profit = payoff + price*e^{r*t}-S

Value

A list of two components.

Note

Finds the put price by using the Black Scholes equation by default.

See Also

option.call

covered.put

Examples

covered.call(S=100,K=110,r=.03,t=1,sd=.2,plot=TRUE)

Covered Put

Description

Gives a table and graphical representation of the payoff and profit of a covered put strategy for a range of future stock prices.

Usage

covered.put(S,K,r,t,sd,price=NA,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K: payoff =S-K

For S_t>K: payoff =S-S_t

profit = payoff + price*e^{r*t}

Value

A list of two components.

Note

Finds the put price by using the Black Scholes equation by default.

See Also

option.put

covered.call

Examples

covered.put(S=100,K=110,r=.03,t=1,sd=.2,plot=TRUE)

Forward Contract

Description

Gives a table and graphical representation of the payoff of a forward contract, and calculates the forward price for the contract.

Usage

forward(S,t,r,position,div.structure="none",dividend=NA,df=1,D=NA,k=NA,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position: payoff = S_t - forward price

Short Position: payoff = forward price - S_t

If div.structure = "none"

forward price=S*e^{r*t}

If div.structure = "discrete"

eff.i=e^r-1

j=(1+eff.i)^{\frac{1}{df}}-1

Number of dividends: t^*=t*df

if k = NA: forward price =S*e^{r*t}-dividend*{s_{\left. {\overline {\, t^* \,}}\! \right |j}}

if k != j: forward price =S*e^{r*t}-dividend*\frac{1-(\frac{1+k}{1+j})^{t^*}}{j-k}*e^{r*t}

if k = j: forward price =S*e^{r*t}-dividend*\frac{t^*}{1+j}*e^{r*t}

If div.structure = "continuous"

forward price=S*e^{(r-D)*t}

Value

A list of two components.

Note

Leave an input variable as NA if it is not needed (ie. k=NA if div.structure="none").

See Also

forward.prepaid

Examples

forward(S=100,t=2,r=.03,position="short",div.structure="none")

forward(S=100,t=2,r=.03,position="long",div.structure="discrete",dividend=3,k=.02)

forward(S=100,t=1,r=.03,position="long",div.structure="continuous",D=.01)

Prepaid Forward Contract

Description

Gives a table and graphical representation of the payoff of a prepaid forward contract, and calculates the prepaid forward price for the contract.

Usage

forward.prepaid(S,t,r,position,div.structure="none",dividend=NA,df=1,D=NA,
k=NA,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position: payoff = S_t - prepaid forward price

Short Position: payoff = prepaid forward price - S_t

If div.structure = "none"

forward price=S

If div.structure = "discrete"

eff.i=e^r-1

j=(1+eff.i)^{\frac{1}{df}}-1

Number of dividends: t^*=t*df

if k = NA: prepaid forward price =S-dividend*{a_{\left. {\overline {\, t^* \,}}\! \right |j}}

if k != j: prepaid forward price =S-dividend*\frac{1-(\frac{1+k}{1+j})^{t^*}}{j-k}

if k = j: prepaid forward price =S-dividend*\frac{t^*}{1+j}

If div.structure = "continuous"

prepaid forward price=S*e^{-D*t}

Value

A list of two components.

Note

Leave an input variable as NA if it is not needed (ie. k=NA if div.structure="none").

See Also

forward

Examples

forward.prepaid(S=100,t=2,r=.04,position="short",div.structure="none")

forward.prepaid(S=100,t=2,r=.03,position="long",div.structure="discrete",
dividend=3,k=.02,df=2)

forward.prepaid(S=100,t=1,r=.05,position="long",div.structure="continuous",D=.06)

Call Option

Description

Gives a table and graphical representation of the payoff and profit of a long or short call option for a range of future stock prices.

Usage

option.call(S,K,r,t,sd,price=NA,position,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position:

payoff = max(0,S_t-K)

profit = payoff - price*e^{r*t}

Short Position:

payoff = -max(0,S_t-K)

profit = payoff + price*e^{r*t}

Value

A list of two components.

Note

Finds the call price by using the Black Scholes equation by default.

Author(s)

Kameron Penn and Jack Schmidt

See Also

option.put

bls.order1

Examples

option.call(S=100,K=110,r=.03,t=1.5,sd=.2,price=NA,position="short")

option.call(S=100,K=100,r=.03,t=1,sd=.2,price=10,position="long")

Put Option

Description

Gives a table and graphical representation of the payoff and profit of a long or short put option for a range of future stock prices.

Usage

option.put(S,K,r,t,sd,price=NA,position,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position:

payoff = max(0,K-S_t)

profit = payoff-price*e^{r*t}

Short Position:

payoff = -max(0,K-S_t)

profit = payoff+price*e^{r*t}

Value

A list of two components.

Note

Finds the put price by using the Black Scholes equation by default.

Author(s)

Kameron Penn and Jack Schmidt

See Also

option.call

bls.order1

Examples

option.put(S=100,K=110,r=.03,t=1,sd=.2,price=NA,position="short")

option.put(S=100,K=110,r=.03,t=1,sd=.2,price=NA,position="long")

Arithmetic Perpetuity

Description

Solves for the present value, amount of the first payment, the payment increment amount per period, or the interest rate for an arithmetically growing perpetuity.

Usage

perpetuity.arith(pv=NA,p=NA,q=NA,i=NA,ic=1,pf=1,imm=TRUE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Perpetuity Immediate:

pv=\frac{p}{j}+\frac{q}{j^2}

Perpetuity Due:

pv=(\frac{p}{j}+\frac{q}{j^2})*(1+j)

Value

Returns a matrix of input variables, and calculated unknown variables.

Note

One of pv, p, q, or i must be NA (unknown).

Author(s)

Kameron Penn and Jack Schmidt

See Also

perpetuity.geo

perpetuity.level

annuity.arith

annuity.geo

annuity.level

Examples

perpetuity.arith(100,p=1,q=.5,i=NA,ic=1,pf=1,imm=TRUE)

perpetuity.arith(pv=NA,p=1,q=.5,i=.07,ic=1,pf=1,imm=TRUE)

perpetuity.arith(pv=100,p=NA,q=1,i=.05,ic=.5,pf=1,imm=FALSE)

Geometric Perpetuity

Description

Solves for the present value, amount of the first payment, the payment growth rate, or the interest rate for a geometrically growing perpetuity.

Usage

perpetuity.geo(pv=NA,p=NA,k=NA,i=NA,ic=1,pf=1,imm=TRUE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Perpetuity Immediate:

j > k: pv=\frac{p}{j-k}

Perpetuity Due:

j > k: pv=\frac{p}{j-k}*(1+j)

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

One of pv, p, k, or i must be NA (unknown).

See Also

perpetuity.arith

perpetuity.level

annuity.arith

annuity.geo

annuity.level

Examples

perpetuity.geo(pv=NA,p=5,k=.03,i=.04,ic=1,pf=1,imm=TRUE)

perpetuity.geo(pv=1000,p=5,k=NA,i=.04,ic=1,pf=1,imm=FALSE)

Level Perpetuity

Description

Solves for the present value, interest rate, or the amount of the payments for a level perpetuity.

Usage

perpetuity.level(pv=NA,pmt=NA,i=NA,ic=1,pf=1,imm=TRUE)

Arguments

Details

Effective Rate of Interest: eff.i=(1+\frac{i}{ic})^{ic}-1

j=(1+eff.i)^{\frac{1}{pf}}-1

Perpetuity Immediate:

pv=pmt*{a_{\left. {\overline {\, \infty \,}}\! \right |j}}=\frac{pmt}{j}

Perpetuity Due:

pv=pmt*{\ddot {a}_{\left. {\overline {\, \infty \,}}\! \right |j}}=\frac{pmt}{j}*(1+i)

Value

Returns a matrix of the input variables and calculated unknown variables.

Note

One of pv, pmt, or i must be NA (unknown).

Author(s)

Kameron Penn and Jack Schmidt

See Also

perpetuity.arith

perpetuity.geo

annuity.arith

annuity.geo

annuity.level

Examples

perpetuity.level(pv=100,pmt=NA,i=.05,ic=1,pf=2,imm=TRUE)

perpetuity.level(pv=100,pmt=NA,i=.05,ic=1,pf=2,imm=FALSE)

Protective Put

Description

Gives a table and graphical representation of the payoff and profit of a protective put strategy for a range of future stock prices.

Usage

protective.put(S,K,r,t,sd,price=NA,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K: payoff =K-S

For S_t>K: payoff =S_t-S

profit = payoff - price*e^{r*t}

Value

A list of two components.

Note

Finds the put price by using the Black Scholes equation by default.

Author(s)

Kameron Penn and Jack Schmidt

See Also

option.put

Examples

protective.put(S=100,K=100,r=.03,t=1,sd=.2)

protective.put(S=100,K=90,r=.01,t=.5,sd=.1)

Interest, Discount, and Force of Interest Converter

Description

Converts given rate to desired nominal interest, discount, and force of interest rates.

Usage

rate.conv(rate, conv=1, type="interest", nom=1)

Arguments

Details

1+i=(1+\frac{i^{(n)}}{n})^n=(1-d)^{-1}=(1-\frac{d^{(m)}}{m})^{-m}=e^\delta

Value

A matrix of the interest, discount, and force of interest conversions for effective, given and desired conversion rates.

The row named 'eff' is used for the effective rates, and the nominal rates are in a row named 'nom(x)' where the rate is convertible x times per year.

Author(s)

Kameron Penn and Jack Schmidt

Examples

rate.conv(rate=.05,conv=2,nom=1)

rate.conv(rate=.05,conv=2,nom=4,type="discount")

rate.conv(rate=.05,conv=2,nom=4,type="force")

Straddle Spread

Description

Gives a table and graphical representation of the payoff and profit of a long or short straddle for a range of future stock prices.

Usage

straddle(S,K,r,t,price1,price2,position,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position:

For S_t<=K: payoff =K-S_t

For S_t>K: payoff =S_t-K

profit = payoff - (price1 + price2)*e^{r*t}

Short Position:

For S_t<=K: payoff =S_t-K

For S_t>K: payoff =K-S_t

profit = payoff + (price1 + price2)*e^{r*t}

Value

A list of two components.

See Also

straddle.bls

option.put

option.call

strangle

Examples

straddle(S=100,K=110,r=.03,t=1,price1=15,price2=10,position="short")

Straddle Spread - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a long or short straddle for a range of future stock prices. Uses the Black Scholes equation for the call and put prices.

Usage

straddle.bls(S,K,r,t,sd,position,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

Long Position:

For S_t<=K: payoff =K-S_t

For S_t>K: payoff =S_t-K

profit = payoff-(price_{call}+price_{put})*e^{r*t}

Short Position:

For S_t<=K: payoff =S_t-K

For S_t>K: payoff =K-S_t

profit = payoff+(price_{call}+price_{put})*e^{r*t}

Value

A list of two components.

See Also

option.put

option.call

strangle.bls

Examples

straddle.bls(S=100,K=110,r=.03,t=1,sd=.2,position="short")

straddle.bls(S=100,K=110,r=.03,t=1,sd=.2,position="long",plot=TRUE)

Strangle Spread

Description

Gives a table and graphical representation of the payoff and profit of a long strangle spread for a range of future stock prices.

Usage

strangle(S,K1,K2,r,t,price1,price2,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =K1-S_t

For K1<S_t<K2: payoff =0

For S_t>=K2: payoff =S_t-K2

profit = payoff - (price1 + price2)*e^{r*t}

Value

A list of two components.

Note

K1 < S < K2 must be true.

Author(s)

Kameron Penn and Jack Schmidt

See Also

strangle.bls

option.put

option.call

straddle

Examples

strangle(S=105,K1=100,K2=110,r=.03,t=1,price1=10,price2=15,plot=TRUE)

Strangle Spread - Black Scholes

Description

Gives a table and graphical representation of the payoff and profit of a long strangle spread for a range of future stock prices. Uses the Black Scholes equation for the call prices.

Usage

strangle.bls(S,K1,K2,r,t,sd,plot=FALSE)

Arguments

Details

Stock price at time t =S_t

For S_t<=K1: payoff =K1-S_t

For K1<S_t<K2: payoff =0

For S_t>=K2: payoff =S_t-K2

profit = payoff-(price_{K1}+price_{K2})*e^{r*t}

Value

A list of two components.

Note

K1 < S < K2 must be true.

Author(s)

Kameron Penn and Jack Schmidt

See Also

option.put

option.call

straddle.bls

Examples

strangle.bls(S=105,K1=100,K2=110,r=.03,t=1,sd=.2)

strangle.bls(S=115,K1=50,K2=130,r=.03,t=1,sd=.2)

Commodity Swap

Description

Solves for the fixed swap price, given the variable prices and interest rates (either as spot rates or zero coupon bond prices).

Usage

swap.commodity(prices, rates, type="spot_rate")

Arguments

Details

For spot rates: \sum_{k=1}^n\frac{prices_k}{(1+rates_k)^k}=\sum_{k=1}^n\frac{X}{(1+rates_k)^k}

For zero coupon bond prices: \sum_{k=1}^nprices_k*rates_k=\sum_{k=1}^nX*rates_k

Where X= fixed swap price.

Value

The fixed swap price.

Note

Length of the price vector and rate vector must be of the same length.

Author(s)

Kameron Penn and Jack Schmidt

See Also

swap.rate

Examples

swap.commodity(prices=c(103,106,108), rates=c(.04,.05,.06))

swap.commodity(prices=c(103,106,108), rates=c(.9615,.907,.8396),type="zcb_price")

swap.commodity(prices=c(105,105,105), rates=c(.85,.89,.80),type="zcb_price")

Interest Rate Swap

Description

Solves for the fixed interest rate given the variable interest rates (either as spot rates or zero coupon bond prices).

Usage

swap.rate(rates, type="spot_rate")

Arguments

Details

For spot rates: 1=\sum_{k=1}^n[\frac{R}{(1+rates_k)^k}]+\frac{1}{(1+rates_n)^n}

For zero coupon bond prices: 1=\sum_{k=1}^n(R*rates_k)+rates_n

Where R= fixed swap rate.

Value

The fixed interest rate swap.

See Also

swap.commodity

Examples

swap.rate(rates=c(.04, .05, .06), type = "spot_rate")

swap.rate(rates=c(.93,.95,.98,.90), type = "zcb_price")

Dollar Weighted Yield

Description

Calculates the dollar weighted yield.

Usage

yield.dollar(cf, times, start, end, endtime)

Arguments

Details

I=end-start-\sum_{k=1}^ncf_k

i^{dw}=\frac{I}{start*endtime-\sum_{k=1}^ncf_k*(endtime-times_k)}

Value

The dollar weighted yield.

Note

Time of comparison (endtime) must be larger than any number in vector of cash flow times.

Length of cashflow vector and times vector must be equal.

See Also

yield.time

Examples

yield.dollar(cf=c(20,10,50),times=c(.25,.5,.75),start=100,end=175,endtime=1)

yield.dollar(cf=c(500,-1000),times=c(3/12,18/12),start=25200,end=25900,endtime=21/12)

Time Weighted Yield

Description

Calculates the time weighted yield.

Usage

yield.time(cf,bal)

Arguments

Details

i^{tw}=\prod_{k=1}^n (\frac{bal_{1+k}}{bal_k+cf_k})-1

Value

The time weighted yield.

Note

Length of cash flows must be one less than the length of balances.

If lengths are equal, it will not use final cash flow.

Author(s)

Kameron Penn and Jack Schmidt

See Also

yield.dollar

Examples

yield.time(cf=c(0,200,100,50),bal=c(1000,800,1150,1550,1700))