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I have a bit of trouble understanding how to determine the replicating portfolio of a call using just a stock and the riskfree asset.

I have times $t = 0,1,2$, and at time $2$, we have $3$ payoffs ($(69, 4, 0)$), at time $1$ the arbitrage-free prices are $18$ and $0.8$, and at time $0$, the arbitrage-free price of the call is $4$. (Note that this is just a two-period binomial tree).

How do I determine the replicating self-financing portfolio, both what is needed to be held at time $0$ and what is needed to be held at time $1$? All the other values (stock prices, rate of return on riskfree asset, and equivalent martingale measures) are available as well. I would prefer an answer based on this simple example as opposed to an answer using some theorem which I have not heard of.

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  • $\begingroup$ what is today's stock price? $\endgroup$ – Gordon Jun 2 '16 at 19:20

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