der-chap3 - Math 618 Notes Chapter 3 Buying Insurance:...

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Unformatted text preview: Math 618 Notes Chapter 3 Buying Insurance: floors (put) and caps (call) Selling Insurance: covered writing (call or put) v.s. naked writing Synthetic Forward: buy a C(K,T) and sell a P(K,T). Put-Call Parity: Present value of the cost to buy a share at t = T by a synthetic forward: C(K, T ) - P (K, t) + PV (K) Present value of the cost to buy a share at t = T by a forward contract: PV (F0,T ) = C(K, T ) - P (K, t) = PV (F0,T - K) In a simple case (no dividend, no spread, continuous rate ...) C(K, T ) - P (K, t) = S0 - e-rT K Spreads Bull Spread Purchase a call C(K, T ) and write a call C(K , T ) with K > K: $ $ T K E r r ST K d d d T r r = K K E ST Bear Spread Write a put P (K, T ) and purchase a put P (K , T ) with K > K Box Spread Long and short synthetic forwards with different prices: $ $ T d d d dr r K K d d T E d d ST = K K r r E ST Collars Purchase a P (K, T ) and write a C(K , T ) with K > K: $ $ T d d dr K r K d d d d E ST T d d = dr K r K d d d d E ST width, zero-cost collar, ... Straddles Purchase a P (K, T ) and a C(K, T ): $ $ T d d d dr E d K T d d d d r d K E ST ST = Strangles Purchase a P (K, T ) and a C(K , T ) with K > K: $ $ T d d dr r KK T E ST d d = dr r KK E ST Butterfly Spreads Purchase a C(K, T ) and a C(K , T ) with K > K, write two C K+K 2 ,T ...
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This note was uploaded on 02/27/2012 for the course FINANCE 101 taught by Professor Yuy during the Spring '12 term at Centenary College New Jersey.

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der-chap3 - Math 618 Notes Chapter 3 Buying Insurance:...

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