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**Unformatted text preview: **Notes 13 Interest Rate Derivatives: Standard Model Learning objectives 1. Understand the use of the Black Model and it validity in the pricing of options 2. Have knowledge of the different type of embedded options 3. Be able to apply the Black Model to value bond options 4. Understand what interest rate cap and floors are and their application and valuation 5. Understand and be able to value Swaptions. 6. Understand the difficulties of a yield curve shift in evaluating derivatives Why is the valuation of options on interest rate derivative so complicated? 1. Term Structure of interest rates is not flat 2. Volatility generally varies with maturity 3. Interest rate stochastic processes are more complicated due to the term structure 4. The term structure is used both the defining the payouts of the derivative and the discounting mechanism. The basic Black Model K : strike price F 0 : forward value of variable today T : option maturity : volatility of F With a delayed payment the equation above modified the T value in the first two equations is the time to when the payout is made rather the expiration of the option. The option might be written to expire in six months but the actual delivery of the underlying asset would take place in 7 months if the option is exercised. The time in the above top two equations would be the 7 month actual delivery A bond option is an option to buy/sell a certain bond by a particular date for a set price. There is a very active bond options market that is over the counter. Other instance of bond options are those embedded in bond indenture agreement. 1. Corporate bonds that are callable A corporate bond which has the ability to be retired at certain date by the company is said to be callable and can be thought of from the buyer point of view as long a bond and short a call option. The is usually a period sometimes called the lockout period or deferred call that for corporate bonds prevent the issuer 1 2 2 1 2 1 2 1 (0, )[ ( ) ( )] (0, )[ ( ) (...

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