Bond-Pricing; Black Scholes

Description Usage Arguments Details Value

Compute values of call and put options as well as the Greeks - the sensitivities of the option price to various input arguments using the Generalized Black Scholes model. "Generalized" means that the asset can have a continuous dividend yield.

1	GenBS(s, X, r, Sigma, t, div_yield = 0)

`s`	the spot price of the asset (the stock price for options on stocks)
`X`	the exercise or strike price of the option
`r`	the continuously compounded rate of interest in decimal (0.10 or 10e-2 for 10%) (use `equiv.rate` to convert to a continuously compounded rate)
`Sigma`	the volatility of the asset price in decimal (0.20 or 20e-2 for 20%)
`t`	the maturity of the option in years
`div_yield`	the continuously compounded dividend yield (0.05 or 5e-2 for 5%) (use `equiv.rate` to convert to a continuously compounded rate)

The Generalized Black Scholes formula for call options is
exp(-r * t) * (s * exp(g * t) * Nd1 - X * Nd2)
where
g = r - div\_yield
Nd1 = N(d1) and Nd2 = N(d2)
d1 = (log(s / X) + (g + Sigma^2/ 2) * t) / (Sigma * sqrt(t))
d2 = d1 - Sigma * sqrt(t)
N denotes the normal CDF (pnorm)
For put options, the formula is
exp(-r * t) * (-s * exp(g * t) * Nminusd1 + X * Nminusd2)
where
Nminusd1 = N(-d1) and Nminusd2 = N(-d2)

A list of the following elements

`call`	the value of a call option
`put`	the value of a put option
`Greeks`	a list of the following elements
`Greeks$callDelta`	the delta of a call option - the sensitivity to the spot price of the asset
`Greeks$putDelta`	the delta of a put option - the sensitivity to the spot price of the asset
`Greeks$callTheta`	the theta of a call option - the time decay of the option value with passage of time. Note that time is measured in years. To find a daily theta divided by 365.
`Greeks$putTheta`	the theta of a put option
`Greeks$Gamma`	the gamma of a call or put option - the second derivative with respect to the spot price or the sensitivity of delta to the spot price
`Greeks$Vega`	the vega of a call or put option - the sensitivity to the volatility
`Greeks$callRho`	the rho of a call option - the sensitivity to the interest rate
`Greeks$putRho`	the rho of a put option - the sensitivity to the interest rate
`extra`	a list of the following elements
`extra$d1`	the d1 of the Generalized Black Scholes formula
`extra$d2`	the d2 of the Generalized Black Scholes formula
`extra$Nd1`	is `pnorm`(d1)
`extra$Nd2`	is `pnorm`(d2)
`extra$Nminusd1`	is `pnorm`(-d1)
`extra$Nminusd2`	is `pnorm`(-d2)
`extra$callProb`	the (risk neutral) probability that the call will be exercised = `Nd2`
`extra$putProb`	the (risk neutral) probability that the put will be exercised = `Nminusd2`