Fm3_chapter17 - UN-11CBINOMIAL OPTION PRICING IN A ONE-PERIOD MODELUp U1.10Down D0.97Initial stock price50.00Interest rate R1.06Exercise

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Unformatted text preview: UN-11CBINOMIAL OPTION PRICING IN A ONE-PERIOD MODELUp, U1.10Down, D0.97Initial stock price50.00Interest rate, R1.06Exercise price50.00Stock priceBond price55.00#MACRO?1.06#MACRO?50.001.0048.50#MACRO?1.06#MACRO?Call option5.00#MACRO????0.00#MACRO?Solving the portfolio problem: A shares + B bonds combine to give option payoffsA0.7692###B-35.1959###Call price3.2656###ABCDEFGHIJ1234567891011121314151617181920212223DERIVING THE STATE PRICESUp, U1.10Down, D0.97Interest rate, R1.06State prices0.6531#MACRO?0.2903#MACRO?Check: Confirm that state prices actually price the stock and the bond1#MACRO?1.06#MACRO?qUqDPricing the stock: 1 = qU*U+qD*D?Pricing the bond: 1/R = qU+qD?ABC123456789101112Up, U1.10Down, D0.97Interest rate, R1.06Initial stock price, S50.00Option exercise price, X50.00State prices0.65310.2903Pricing the call and the putCall price3.2656Put price0.4354Put-call parityStock + put50.4354Call + PV(X)50.4354BINOMIAL OPTION PRICING WITH (TWO-DATEqUqDNote about PV(X) in put-call parity:In the continuous-time framework (the standard Black-Scframework here is discrete time, PV(X) is also discrete-tiAB1234567891011121314151617181920#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?STATE PRICES IN A ONE-PERIOD E) MODELcholes framework), PV(X) = X*Exp(-r*T). Because the ime: PV(X)=X/(1+r)=X/R.C1234567891011121314151617181920Pricing by state pricesPricing by risk-neutral pricesEQUIVALENCE OF PRICING BY STATE PRICES AND RISK-NEUTRAL PRICESXUqU*XU+qD*XDXDXU(πU*XU+πD*XD)/RXDRelation of risk-neutral to state prices: πU=qU*R, πD= qD*RRISK-NEUTRAL PRICUp, U1.10Down, D0.97Interest rate, R1.06Initial stock price, S50.00Option exercise price, X50.00State prices0.65310.2903Risk-neutral prices0.69230.3077Pricing the call and the put using state pricesCall price3.2656Put price0.4354Pricing the call and the put using risk-neutral pricesCall price3.2656Put price0.4354qUqDπU = qU*RπD = qD*RAB12345678910111213141516171819202122CES OR STATE PRICES?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?#MACRO?C12345678910111213141516171819202122UN-11HUp, U1.10Down, D0.97State pricesInterest rate, R1.060.6531###Initial stock price, S50.000.2903###Option exercise price, X50.00Stock priceBond price60.50001.123655.00001.060050.000053.35001.001.123648.50001.060047.04501.1236Call option price10.5000###7.83025.74923.3500###2.18800.0000###BINOMIAL OPTION PRICING WITH STATE PRICES IN A TWO-PERIOD (THREE-DATE) MODELqUqD=qU*E18+qD*E20=qU*C19+qD*C21=qU*E20+qD*E22ABCDEFGHIJK12345678910111213141516171819202122232425262728293031323334UN-11HABCDEFGHIJK35363738394041424344454647484950515253545556575859606162636465666768697071UN-11HABCDEFGHIJK72737475767778798081828384858687888990919293949596979899100101102103104105106107108UN-11HABCDEFGHIJK109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145UN-11HABCDEFGHIJK146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182UN-11HABCDEFGHIJK183184...
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This note was uploaded on 01/23/2011 for the course FGB 780 taught by Professor Edwardchang during the Spring '09 term at Missouri State University-Springfield.

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Fm3_chapter17 - UN-11CBINOMIAL OPTION PRICING IN A ONE-PERIOD MODELUp U1.10Down D0.97Initial stock price50.00Interest rate R1.06Exercise

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