Systems and methods for determining a present value of an option on a security having a fixed cash flow leg based upon a Martingale. The Martingale may be based upon a ratio of the present value of the option and a numeraire. The numeraire may be a coupon annuity which may be based on coupons of the security post expiry of the option, accrual periods of the coupon, and spread-adjusted discount factors for coupon dates of the option. The spread-adjusted discount factor may be based on an instantaneous forward rate and a time-varying spread. The present value of the option may be determined based upon a spread, a notional value of the security, and an expectation of a maximum value of (1) a difference between an artificial strike coupon and a forward swap rate and (2) zero. This spread may equal a difference between the forward swap rate and a strike coupon or the strike coupon divided by the forward swap rate.
展开▼
