The black scholes formula

Question 1

Elaborate on the parts of hte black scholes formula

Answer 1

We have:

C = S e^(-∂T) N(d1) - K e^(-rT) N(d2)

Question 2

elaborate on the assumptions of BS model

Answer 2

1) Continuously compounded returns are normalyl distributed
2) volatility of continously compounded returns are known and constant
3) Future dividends are known, either as fixed yield or dollar amount

easy to borrow/short
no transacation costs
constant and known risk free rate

Question 3

elaborate on gamma hedging

Answer 3

we cannot do this using just the stock itself, because the gamma of a stock is 0.

we typically therefore need to use options to make a position gamma neutral. Then we can make it delta-neutral by using shares later.

If we have one call option, and have gamma exposure of 0.1, and some other option has exposure of 0.2, if we long the first we need to short 0.5 of the other.