butterfly.spread.bls: Butterfly Spread - Black Scholes
In FinancialMath: Financial Mathematics for Actuaries

Description Usage Arguments Details Value Note See Also Examples

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.

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

`S`	spot price at time 0
`K1`	strike price of the first long call
`K2`	strike price of the two short calls
`K3`	strike price of the second long call
`r`	continuously compounded yearly risk free rate
`t`	time of expiration (in years)
`sd`	standard deviation of the stock (volatility)
`plot`	tells whether or not to plot the payoff and profit

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}

A list of two components.

`Payoff`	A data frame of different payoffs and profits for given stock prices.
`Premiums`	A matrix of the premiums for the call options and the net cost.

K2 must be equal to S.

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

K1 < K2 < K3 must be true.

butterfly.spread

option.call