SOA Sample #18

[enirehtac07]

I'm not sure if a thread already exists for this problem, but I'll post it anyway.
-----------------------
A market-maker sells 1,000 1-year European gap call options, and delta-hedges the position with shares. You are given:

Each gap call option is written on 1 share of a nondividend-paying stock.
The current price of the stock is 100.
The stock's volatility is 100%.
Each gap call option has a strike price of 130.
Each gap call option has a payment trigger of 100.
The risk-free interest rate is 0%.

Under the Black-Scholes framework, determine the initial number of shares in the delta-hedge.
-----------------------

The solution uses:
delta_gap = delta_regular call - 30*N'(d2)/(S*sigma*sqrt(T))

I understand this formula except for the last part - why is the second term being divided by S*sigma*sqrt(T)?

Thanks!!

-----------------------
ANS: 586

[its_me]

Search for the post where jraven derives it step-by-step.

[blahbla]

Originally Posted by enirehtac07

I'm not sure if a thread already exists for this problem, but I'll post it anyway.
-----------------------
A market-maker sells 1,000 1-year European gap call options, and delta-hedges the position with shares. You are given:

Each gap call option is written on 1 share of a nondividend-paying stock.
The current price of the stock is 100.
The stock's volatility is 100%.
Each gap call option has a strike price of 130.
Each gap call option has a payment trigger of 100.
The risk-free interest rate is 0%.

Under the Black-Scholes framework, determine the initial number of shares in the delta-hedge.
-----------------------

The solution uses:
delta_gap = delta_regular call - 30*N'(d2)/(S*sigma*sqrt(T))

I understand this formula except for the last part - why is the second term being divided by S*sigma*sqrt(T)?

Thanks!!

-----------------------
ANS: 586

lol i actually spent about an hour deriving delta for a regular black scholes call the long way....that was awesome..JK!

the partial derivative with respect to S of 30N(d2) is equal to

30*N'(d2)* d (d2)/dS that 1/S*sigma*sqrt(T) is d/dS(d2)

[badmaj5]

anyone know how the end result would look for delta_gap if we were looking at a put instead of a call in this problem?

[blahbla]

Originally Posted by badmaj5

anyone know how the end result would look for delta_gap if we were looking at a put instead of a call in this problem?

it would come out to be 1 - delta of the gap call

Originally Posted by its_me

Search for the post where jraven derives it step-by-step.