Question

Interpretation of the Black-Scholes model. What is the hedge ratio for a call (put) option and what is the probability that a call (put) option finishes in the money?

Answer 1

Black Scholes Model is pricing model used to ascertain the fair price or theroretical value for a call or put option based volatility , type of option , underlying stock price , time , strike price and risk free rate.

The model is largely used by Option traders who buy options that are priced under formula calculated value and sell options that are priced higher than calculated value

The formula for computing Option price is as below

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

Put Option Premium P = Xe - rT N (-d2) S0 N (-d1)

C is price of a call option

P is price of Put Option

S is price of the Underlying Asset

X is Strike price of the option

r is rate of Interest

t is time to expiration

s is volatility of the underlying

N is a standard normal distribution with mean =0 and SD =1

Hedge ratio for a call put option is the ratio of exposure to a hedging instrument to the value of hedged asset. It is an important statistic in risk management since it will identify extent to the which the risk of any adverse movement in our asset or liability will be met by the offsetting movement in the hedging instrument.

These equations gives the probability of a successful trade for a

European put finishing in the money that the probability that the strike price is above the market price at maturity.