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So the question asks: Given a 3-steps Binomial Tree model with $S(0) = 50$, $U = 20%,D = 20%$, and $R = 5%$. A European call option has the strike price $X = 40$ and maturity time $T = 3$. Also, a Put-on-Call option is written on this European call option with maturity time T = 2, i.e, the final payoff (at T = 2) of PoC option is given by H(T) = max ($K_p -C_E(2), 0)$, where $C_E(2)$ is the value (price) of the underlying European call option at T = 2. The strike price of the outside put option $K_p = 12$. Find out the initial price of this Put-on-Call option.

So so far I have: enter image description here enter image description here Where I constructed the binomial tree model for the European call option only ( without the put-on-call option). So I got the European call option price is $16.4669042$.

But what exactly is the $C_E(2)$, the value (price) of the underlying European call option at T = 2?

Is it C(2) = max{0, 0.5(S(1)+S(2)) - X}? If so I then have three C(2)?

Also, what is the final payoff H(T) at T=2? Where should it go on the graph?

Betty
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  • Exact duplicate of http://quant.stackexchange.com/questions/25102/put-on-call-option-confusion –  Mar 27 '16 at 17:33
  • Not sure I am following. In your universe there are three possible states of the world at time $T=2$, according to the price of the underlying. In one of those states, the call is worthless (as the underlying has no hope of getting above $40$ in the one remaining time interval). In the other two states it has values which you can read off from your top tree (being sure to discount appropriately). – lulu Mar 27 '16 at 17:35
  • Oh, I think I understand your comment "If so I then have three C(2)?". Yes. You get a different value for the call in each of the possible states of the world. If you liked, you could use your tree to compute the forward price of the call (i.e. the expected value of the call at $T=2$). – lulu Mar 27 '16 at 17:38

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I am not sure I fully understand your question, but you use the second tree to find an option prices as a weighted average of prices of leaves at the same time eg 2. The weights are your chances to get there...

Vlad Z
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