3. Suppose the 1 year interest rate is 6%. Suppose a 1000 strike 3 year call costs $172. At what price of the underlying stock is the payoff from a long call position the same as the payoff from a short call position. (Don't forget interest.)
The price above 1000 adjusted for interest rate in 3 years at
which profit in present terms would be 172 is strike price plus FV
of 172 after 3 years
=1000+(172*(1.06)^3))=204.85
=1204.85
At this price payoff from long call is zero as it will be similar
to getting 172 in present terms which will cover for the premium of
the call option.
Now shorting the call option will make one receive 172 in present
terms which will have to be rapaid as a profit on call option at
that price
Hence answer = $1,204.85
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