Suppose now that we had a continuum of states – say the state could be any positive number. Consider some arbitrary asset with price S(x). Assume…

Suppose now that we had a continuum of states – say the state could be any positive number.

a. Consider some arbitrary asset with price S(x). Assume that S is strictly increasing and differentiable. In fact, to simplify matters, assume that S(x)=x; that is, we name the state x after the price of our asset in this state, S(x). Let c(k) be the price of a call option on this asset with strike price k. Using the decomposition principle, write down an explicit formula for c(k).

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b. What can you say about the second derivative of this price c’’(k)?

c. Suppose you observe the following prices of call options on some stock:

strike 1 2  345   67

price of call  7.01 5.46 4.88 4.46 3.30 1.55 1.02

Can you do arbitrage? How?

The post Suppose now that we had a continuum of states – say the state could be any positive number. Consider some arbitrary asset with price S(x). Assume… first appeared on Brainy Term Papers.

Suppose now that we had a continuum of states – say the state could be any positive number. Consider some arbitrary asset with price S(x). Assume… was first posted on October 8, 2020 at 5:26 pm.
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