# A4 - ACTSC/STAT 446/846 Assignment#4 Due date April 3rd...

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ACTSC/STAT 446/846 Assignment #4 Due date: April 3rd, 2009 Note: Recall that, when handing in your assignment, you are requested to use a cover page showing only your UWID number and your section (846 students: also write “846” on the cover page) and to write your full name on the next page. Assignments must be handed in during the TAs office hours before or on the due date (see the Calendar on UW-ACE for details). Let W = { W t , t 0 } be a P -standard Brownian motion. 1. A gap call option is an "option" with payoff X = ( S T - K 1 ) I { S T K 2 } . Compute the premium of this option in Black-Scholes model: (a) if K 1 K 2 ; (b) if K 1 > K 2 . 2. In Black-Scholes model, compute Δ and Γ for a call option. Using put-call parity, compute Δ and Γ for an otherwise identical put option. Explain briefly (and intuitively) what happens to Δ when S 0 is very big/small? 3. A deferred up rebate option with maturity T is an option that pays \$1 at maturity only if the stock price touches/crosses a barrier at level B during the life of the option.

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