blackscholes(amount, exercise, rate, nperiods, sdev, hedge)

There is a 49 U call option with 199 days to maturity on a stock that is selling at present at 50 U. The annualized continuously compounding risk-free interest rate is 7%. The variance of the stock is estimated at 0.09 per year. Using the Black-Scholes model, the value of the option would be

which is about 5.85 U.

Let us examine how this result changes by changing the parameters. Increasing the stock price

the option value increases.

Increasing exercise price

the option value decreases.

Increasing the risk-free interest rate

the option value increases.

Increasing the time to expiration

the option value increases.

Increasing the stock volatility

the option value increases. Plot the value of the call with respect to the share price.

The upper bound: option is never worth more than the share. The lower bound: option is never worth less than what one would get for immediate exercise of the call.

Finance[BlackScholesBinomialTree], Finance[LatticeMethods]