Question

A 9-month American put option on a non-dividend-paying stock has a strike price of $49. The stock price is $50, the risk-free rate is 5% per annum, and the volatility is 30% per annum. Use a three-step binomial tree to calculate the option price.

Answer 1

Solution:

в с D E F 1 2 Inputs call/put? c/p P -1 5 a Asset Strike Time/step, At Volatility, Rf rate, Div yield, a $50.00 Params $49.00 0.25 yrs 30.0% 5.0% 0.0% L p 1- 4 8 9 1.013 50.4% 9.6% 1.162 0.861 d 0.0 1.0 2.0 11 12 13 14 15 16 Stock 3 2 1 0 3 78.42 58.09 43.04 31.88 $67.49 $50.00 $37.04 $58.09 $43.04 $50.00 18 0.0 1.0 2.0 Option 3 3 0 20 Nw 0 $1.43 $7.31 $0.00 $2.92 $11.96 5.96 17.12 $4.289

The price of the option is $4.289

The Formula used are:

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Inputs call/put? c/p P =IF(C3="c",1,-1) Params Asset 50 Strike 49 Time/step, At =3/12 Volatility, 0.3 Rf rate,r 0.05 Div yield, O a =EXP((C9-C10)*c7) p =(E6-E10)/(E9-E10) 1-0 =1-E7 u=EXP|C8*SORT(CZ)) d =EXP(-C8*SQRT(C7)) Stock O 13 14 15 16 3 12 1 O =E14*E9 =E14*E10 =E15*E10 =E16*E10 =D15*$E$9 =D15*$E$10 =D16*$E$10 =C16*$E$9 =C16*$E$10 =C5 | Option o 18 19 20 21 22 3 2 1 =MAX((E14-$C$6)*$D$3,($E$7*F20+($E$8*F21))*EXP(-$C$9*$C$7)) =MAX((D15-$C$6)*$D$3,($E$ 7*E21+($E$8*E22))*EXP(-$C$9*$C$ 7)) =MAX((E15-$C$6)*$D$3,($E$ 7*F21+($E$8*F22))*EXP(-$C$9*$C$ 7)) =MAX((C16-$C$6)*$D$3,($E$ 7*D22+($E$8*D23) *EXP(-$C$9*$C$ 7)) =MAX((D16-$C$6)*$D$3,($E$ 7*E22+($E$8*E23))*EXP(-$C$9*$C$7)) =MAX((E16-$C$6)*$D$3,($E$7*F22+($E$8*F23))*EXP(-$C$9*$C$7)) =MAX($D$3*(F13-$C$6),0) =MAX($D$3*(F14-$C$6),0) =MAX($D$3*(F15-$C$6,0) =MAX($D$3*(F16-$C$6,0) 23 10