In practice, derivatives are numerically approximated using the method of finite differences. For example, the forward difference approximation for a call option delta is given by

() = / 0 ((0 + ) (0)) /

where h is small relative to 0. For the other greeks 0, in the above formula, is changed to the appropriate variable ( for theta, for vega, and for rho).

Consider a put option with a strike price of $110 and 1 year to maturity. Use 199 steps in the binomial model and let the risk-free rate be 5% per annum. The current stock price is $100 with a per annum volatility of 25% and pays no dividends. Use the forward difference approximation, using = $1, to estimate the option Greeks for the European put option on this stock.

What is the absolute difference between the approximated Binomial and Black-Scholes option greeks?

i. Delta

ii. Theta

iii. Vega

iv. Rho