8006 Exam Dumps : Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

Short calls and short puts have negative gamma, ie their delta increases at a decreasing rate as the price of the underlying change. Likewise, remember that long calls and long puts have positive gamma.

A swaption is an option to enter into a fixed for floating interest rate swap at a point in the future, with the fixed rate decided upfront. These options can be European, Bermudan or American, in terms of what dates the option can be exercised. A receiver option on a swap is an option that gives the buyer the right to enter into a swap and receive the fixed rate and pay the variable rate. In the case of a payer option, the buyer pays the fixed rate and receives the variable rate. One way to remember this is that receiving and paying are terms used with reference to the fixed rates.

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.