Chapter 14

# Chapter 14 - UN-11CTWO-DATE BINOMIAL OPTION...

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Unformatted text preview: UN-11CTWO-DATE BINOMIAL OPTION PRICINGUp10%Down-3%Initial stock price50Interest rate6%Exercise price50Stock priceBond price55###1.06<-- =\$G\$12*(1+\$B\$7)50148.5###1.06<-- =\$G\$12*(1+\$B\$7)Call option5###???###A0.7692 <-- =(D16-D18)/(B12*(B3-B4))B-35.1959 <-- =((1+B3)*D18-(1+B4)*D16)/((1+B7)*(B3-B4))Call price3.2656 <-- =C21*B6+C23Check: confirm that state pricesState pricesactually price the stock and the bond0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))1.06###0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))50###Pricing a put and call using the state pricesSolving for the portfolio parameters: A is the number of shares and B is the number of bonds.55*A + 108*B = 548.5*A + 108*B = 0or:A*stock*(1+up)+B*(1+interest)=max(stock*(1+up)-X,0)A*stock*(1+down)+B*(1+interest)=max(stock*(1+down)-X,0)The solution is:check on state pricescall price3.2656023quqdABCDEFGHIJK12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152TWO-DATE BINOMIAL OPTION PRICING WITH STATE PRICESUp10%State pricesDown-3%0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))Initial stock price50Interest rate6%Exercise price50Call payoffIn up state5 <-- =MAX(\$B\$6*(1+B3)-\$B\$8,0)In down state0 <-- =MAX(\$B\$6*(1+B4)-\$B\$8,0)Call price3.2656 <-- =\$E\$4*B11+\$E\$5*B12Put payoffIn up state0 <-- =MAX(\$B\$8-(1+B3)*\$B\$6,0)In down state1.5 <-- =MAX(\$B\$8-(1+B4)*\$B\$6,0)Put price0.4354 <-- =\$E\$4*B16+\$E\$5*B17Put-call parityNote about PV(X) in put-call parity:Stock + put50.4354 <-- =B6+B18In the continuous-time framework (the standardCall + PV(X)50.4354 <-- =B13+B8/(1+B7)Black-Scholes framework), PV(X) = X*Exp(-i*T).Because the framework here is discrete time,PV(X) also has to be discrete-time: PV(X) =X/(1+i) .quqdABCDEFGHIJ12345678910111213141516171819202122232425UN-11HTHREE-DATE BINOMIAL OPTION PRICINGUp10%Down-3%state prices0.6531 <- =(B7-B4)/( 1+B7)*(B3-B4)Initial stock price500.2903 <- =(B3-B7)/( 1+B7)*(B3-B4)Interest rate6%Exercise price50Stock priceBond price60.501.1236551.065053.3511.123648.51.0647.051.1236Cal option price10.507.8305.7493.352.1880.00quqd=qu*E20+qd*E22=qu*C21+qd*C23=qu*E22+qd*E24ABCDEFGHIJK123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225UN-11IFIVE DATE EUROPEAN BINOMIAL OPTION PRICING...
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Chapter 14 - UN-11CTWO-DATE BINOMIAL OPTION...

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