only answer the last red box
Posted: Thu May 19, 2022 12:34 am
only answer the last red box
(1 point) A stock will pay a dividend D att = tp <T, where an American-style put option expires at t =T. This problem values the option by using binomial trees. Because the dividend has known value, for t < to the stock has a non-random component equal the value of dividend, discounted to time t. The dividend is paid at tp, and for t > to the stock price no longer includes this non-random component. To apply the binomial tree method, we construct a binomial tree for the random component of the stock. Then we construct a binomial tree for the stock S by adding the non-random component to the tree for S. Finally we construct the option values, based upon the binomial tree of stock values by working back from t =T. Let So = 86.5 stock price at t = 0 K = 90 strike price for option T 0.0175 risk-free interest rate o 0.21 volatility D=0.56 value of dividend (dollars) tp 0.125 time dividend is paid (years ex-date") T= 0.166667 expiration time (years) M = 2 number of subintervals of time for binomial trees 0.166667 time increment At 2 Let S model the "random" part. Then s(t) = S(t) - Der(tp-t) S(t) 0 <t<td tp <t<T Derto Let S = f(0) = S Between time tě = iAt and txt1, a value š> will increase to $; 11 = uš, with probability p, or š;t1 = aš, with probability 1 – p where = decrease to
u = et = 1.0625, d=e 0.941176, p=(erat - d)/(u – d) = 0.496884. Then values of the "random part" Sare as follows: 52 97.019 š 91.31 85.94 85.94 So 80.88 76.12 Since 5 -|*, s + Der(tp-+-) š) 0 <t; <tp tp <ti <T the binomial tree of asset values is S? 97.019 S 86.5*1.0625 SO 86.5 s2 85.94 Si = 86.5*0.94117€ si = 76.12 At expiration t = T = tą, the option values are V;} = max(K – S},0). Att = ti <T, the option values are Vj = max(K – S), e "At (pV; 1' + (1 - p)V,i+1)) The binomial tree of American put option values is
At expiration t = T = tz, the option values are V;} = max(K - S7,0). Att = ti < T, the option values are v=max(K - S, erAt(pVi!! + (1 - p)Vi+1)) The binomial tree of American put option values is 1,2 0 V 2.0396 VO 5.52512 V? 4.0599 Vo 8.98 V.2 13.87 The approximation to the value of the American put at t = 0 is p Amer 0.58
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u = et = 1.0625, d=e 0.941176, p=(erat - d)/(u – d) = 0.496884. Then values of the "random part" Sare as follows: 52 97.019 š 91.31 85.94 85.94 So 80.88 76.12 Since 5 -|*, s + Der(tp-+-) š) 0 <t; <tp tp <ti <T the binomial tree of asset values is S? 97.019 S 86.5*1.0625 SO 86.5 s2 85.94 Si = 86.5*0.94117€ si = 76.12 At expiration t = T = tą, the option values are V;} = max(K – S},0). Att = ti <T, the option values are Vj = max(K – S), e "At (pV; 1' + (1 - p)V,i+1)) The binomial tree of American put option values is
At expiration t = T = tz, the option values are V;} = max(K - S7,0). Att = ti < T, the option values are v=max(K - S, erAt(pVi!! + (1 - p)Vi+1)) The binomial tree of American put option values is 1,2 0 V 2.0396 VO 5.52512 V? 4.0599 Vo 8.98 V.2 13.87 The approximation to the value of the American put at t = 0 is p Amer 0.58