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To answer a question with a question - are you assuming proportional or constant dividends? :) The general consensus of the market is that dividends are somewhere between proportional (fixed yield) and constant (fixed dollar). The carry embedded into the forward prices at different strikes reflects that consensus, in fact you can establish the ...

6

A simple intuitive answer why the OTM Call is more expensive than the OTM Put is because of the skewness of the log-normal distribution. Think about it, what is the probability that the stock price is above 110 at expiration and what is the probability it is below 90? This should answer your question. Written in probability terms: The median of the ...

5

Dividends are the key. For simplicity, let's include a single dividend at the time of expiration, and assume that the options are European and expire ex. (There is really no reason not to assume that an option on a market index is European. EDIT: not quite true; that's discussed here.) $S+P = e^{-rt}K+C + e^{-rt}D$ This is a certain fixed dividend, but ...

4

The put call parity is given as follows: $$c_t-p_t = S_t - \frac{X}{e^{r(T-t)}}$$ If you assume $r=0$, you get $$c_t-p_t = S_t - X$$ So, $c_t \neq p_t$. The rationale behind it is much more financial than mathematical. You have to look at the payoff on both side of the equation, and you see that both portfolio will give the same payoff at time $T$ (the ...

3

You compare apples and oranges here. You can't possibly compare the profit generated involving S(t) on one side and S(T) on the other side. at time t you do not know what the stock will be worth at time T. Merton made the statement in the context of deciding whether to exercise the call option at any time before expiration OR to simply sell the call ...

1

A logical way of answering this question is proof by contradiction. First note that if it is not optimal to exercise an american option prior to expiry, then the option should have the same value as the european option. So assume that it is not optimal to exercise the option prior to expiry, i.e. assume that the american option has the same value as the ...

1

Look at it the way you would have to realize it, whatever your position in the market is, as the price of a synthetic bond that pays $K$ at time $T$: \begin{array}{c}Ke^{-r(T-t)} & = & S & + & P & -& C \\ (\text{bid}) &=& (\text{bid}) &+& (\text{bid}) &-& (\text{ask})\\ (\text{ask}) &=& (\text{ask}) ...

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