Question

Thoroughly explain Black-Scholes as if you were writing to someone who is reasonably intelligent, but not a finance major or investing expert.

Answer 1

Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or a put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate. The quantum of speculation is more in case of stock market derivatives, and hence proper pricing of options eliminates the opportunity for any arbitrage.

The Black-Scholes Model is used to determine the price of a European call option, which simply means that the option can only be exercised on the expiration date.

Black-Scholes pricing model is largely used by option traders who buy options that are priced under the formula calculated value, and sell options that are priced higher than the Black-Schole calculated value

The formula for computing option price is as under:

Call Option Premium C = SN(d1) - Xe^-rt N(d2)

Put Option Premium P = Xe^-rt N (–d2) – S0 N (-d1)

Here, d1 = [Ln (S / X) + (r + 0.5S²) t] / s

d2 =d1 - s

Here,

C = price of a call option

P = price of a put option

S = price of the underlying asset

X = strike price of the option

r = rate of interest

t = time to expiration

s = volatility of the underlying

N represents a standard normal distribution with mean = 0 and standard deviation = 1

The Black–Scholes formula has only one parameter that cannot be directly observed in the market: the average future volatility of the underlying asset, though it can be found from the price of other options. Since the option value (whether put or call) is increasing in this parameter, it can be inverted to produce a "volatility surface" that is then used to calibrate other models, e.g. for OTC derivatives.