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 |
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 |
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 |
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$Nd1 |
is |
extra$Nd2 |
is |
extra$Nminusd1 |
is |
extra$Nminusd2 |
is |
extra$callProb |
the (risk neutral) probability that the call will be exercised = |
extra$putProb |
the (risk neutral) probability that the put will be exercised = |
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