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From: David-Olivier Tarac
Affiliation: Consultancy
Address: do.tarac@wanadoo.fr
Date: 20 Jul 1998
Time: 16:40:29
Your question is a major issue for financial institutions. The answer is not as obvious as it seems.
First, the maturity of the rate you should use when pricing options should correspond to the maturity of the contract. If the options pays several intermediate cash flows, you have to evaluate them separatly using interest rates of corresponding maturities.
The interest rate reference to be used should account for the default risk of both counterparties inherent in the transaction.
If the option is an asset for your bank (the NPV of the cash flows is positive for your bank), then the appropriate rate to be used should reflect the possible default of your couterparty.
On the countrary, if the option is a liability for your bank, then the appropriate rate should reflect the possibility that your bank fails to honor the term of the option contract. The probability that a bank defaults has been proved to be linked with its refinancing cost (you may visit the site of Pr Lando available on http://www.cob.ohio-state.edu/dept/fin/journal/jof.htm or read the Hull & White's famous "Options, futures and other derivatives"). The rating of the bank is critical regarding this issue since it directly influences the refinancing condition of the institution. The rate to be used will thus be your refinancing cost on the market for the same maturity as the option.
The thing gets more complicated when the derivative you consider is either an asset or a liabilty for your bank, depending on the market conditions. The paradigm of contracts that exhibit such a behaviour is the swap contract. If your bank enters into a plain vanillia swap and agrees to pay a fixed rate, then any interest rates increase should contribute to a positive NPV. The swap will then be an asset for the bank.
On the contrary if interest rates decline, the swap might evolve into a liability for your bank.
Depending on market condition, the appropriate discount rate will thus be either your refinancig cost or your counterparty's refinancing cost. In order to price the derivative properly, one will have to take into account this optional behaviour of the discount rate in his pricing model. For an in depth analysis of this issue, Bob Jarrow published in June 1997 an excellent article about the pricing of a swap with two defautable counteparties.
Best Regards
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