FBE459_3_8_Advanced_Options

FBE459_3_8_Advanced_Options - material not in exam Lecture...

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1 FBE 459 – Financial Derivatives Prof. Pedro Matos Lecture 3.8 (+ 4.3): Advanced Options • Interest Rate Options material not in exam • Credit Derivatives • Structured Finance Readings: HULL chapter 28 Lecture Outline •Interest Rate Options: - Callable Bonds - Swaptions (more in Fixed Income class) • Credit Derivatives: material not in exam 2 - Credit Default Swap • Structured Finance: - Asset Backed Securities - Collateralized Debt Obligations 1. Interest Rate Options Options on securities whose value depends directly on interest rates: . Bond options: callable bonds Bond futures options: T Bond Eurodollar futures 3 . Bond futures options: T-Bond, Eurodollar futures . Options on Loans: limits on rates (caps and floors) . Swaptions . Embedded options on mortgage-backed securities Valuing Interest Rate Derivatives is complicated: . Need an interest rate model for levels of all interest rates (3M, 6M, 1Yr, 5Yr, 10Yr, …) at any time Volatilities of different points on the term 1. Interest Rate Options 4 . Volatilities of different points on the term structure are different . Interest rates are used for discounting the payoff as well as for defining the payoff
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2 (Very simple) Example: . We want to price an European call on a two year pure discount bond, with maturity in T=1 year and strike price K=96. 1. Interest Rate Options 5 . Let’s construct a tree that describes the evolution of the 1-year interest rate. Time period is 1 year. 4% 5% 3% Ex. (cont.) : . Build the bond value tree. Currently, 2-year bond price = 92.278. In 1 year, the 2-year bond will be worth: 95.238 100 1. Interest Rate Options 6 . We can back-out the risk-neutral probability p*=0.605 92.278 97.087 03 . 1 100 05 . 1  087 . 97 *) 1 ( 238 . 95 * 04 . 1 1 278 . 92 p p Ex. (cont.) : . Valuing Call option (K=96, T=1) on 2-year bond 0 1. Interest Rate Options 7 4134 . 0
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FBE459_3_8_Advanced_Options - material not in exam Lecture...

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