# Pricing an exotic IR option

#### tyskland

Hi,
I want to price the following exotic option:

Consider a real estate buyer in the UK. Assume that this buyer, let's call him Peter, decides to buy an apartment for £100 000. Peter doesn't have to pay anything until three months later after the signing of the apartment. To afford this he needs financing through loans. Since I happen to have that kind of money, I offer him the £100 000 in exchange for a fixed interest rate of 4% (which is the current interest rate level at the date of signing) If he buys the option, Peter can after three months do one of the following things

a) Pay me according to the fixed interest rate of 4%
b) Pay me whatever the interest rate is at that day (which is fixed from that day forward)

The catch is that if Peter chooses alternative b) he needs to pay me an amount of £500. In that case the break even level of interest rate is 3.5% (100 000 x BreakEven + 500 = 4 000 => BreakEven = (4 000 – 500) / 100 000 = 0.035 or 3.5%). Hence Peter will chose alternative b) if and only if the interest rate drops below 3.5%.

The problem is: How do you price this type of option? Obviously we would have to know the maturity of the interest rate. Then we would also need some historical data on movements of that particular interest rate.

Any ideas?

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