General Seminar
March 3, 2005, Wednesday, 15:40, Institute of Applied Mathematics, Room S209,
Hayri Körezlioğlu
Institute of Applied Mathematics,METU
On the representation of zero coupon bond prices in terms of random fields
A zero coupon bond with maturity date T, also called a T-bond, is a contract which guarantees the holder 1 YTL to be paid on the date T. The price at time t of a bond with maturity date T is generally represented by
where f is the forward interest rate. Let P be the (historical) probability under which the market is observed. In order to avoid any arbitrage possibility it is supposed that there is a probability Q, equivalent to P, (called the riskneutral probability) under which the discounted bond prices are martingales in t for all T. Martingale properties are expressed with respect to the history of events generated by a basic martingale (e.g., Brownian motion, Brownian sheet, random _field, etc.). The price of any derivative based on the bond prices must be computed under the risk- neutral probability. It is therefore important to know the expression of f under both probabilities P and Q. In this talk this problem will be discussed when f is modelled by a random _field as it naturally appears in the observations.