Think about using binary search and mergesort, or devising your own divide-and-conquer algorithm. Implement and test your algorithm.
Implied volatility. Typically the volatility σ is the unknown value in the Black–Scholes formula (see Exercise 2.1.28). Write a program that reads s, x, r, t, and the current price of the European call option from the command line and uses bisection search to compute σ.
EXERCISE 2.1.28
Black–Scholes option valuation. The Black–Scholes formula supplies the theoretical value of a European call option on a stock that pays no dividends, given the current stock price s, the exercise price x, the continuously compounded risk-free interest rate r, the volatility σ, and the time (in years) to maturity t. The Black–Scholes value is given by the formula s Φ(a) – xe−rtΦ(b),where Φ(z) is the Gaussian cumulative distribution function, a = (ln(s/x) + (r + σ2/2)t)/(σ√t), and b = a − σ√t. Write a program that takes s, r, σ, and t from the command line and prints the Black–Scholes value.
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