Question

You saw an instrument that pays a fixed sum or nothing, depending on whether the underlying is above or below some level at the instrument’s maturity. Can you hedge this instrument? How? Do you see any problems in doing that?

Give a clear explanation

Answer 1

The payoff of such an instrument would be

P(t) = C, if U(t) > Th, where U(t) is the underlying and Th is the threshold

0, if U(t) < Th, where U(t) is the underlying and Th is the threshold

Now coming to question of hedging using this instrument, this instrument is similar to a call option but with a difference that the payoff is fixed and do not increase with increase in the value of the underlying. So it can potentially be used to hedge against an increase in cost of purchasing the underlying.

So for example if the threshold was 50, and the fixed payout was say 30 and the underlying was 40 and for simplicity if the derivative was available at zero price.

Then, net payoff = 0 - 40 = -40

At Th = 50, U =60, net payoff = 30 - 60 = -30

At Th = 50, U =100, net payoff = 30 - 100 = -70

So as we see that the net payoff decreases with increase in asset price and hence using this instrument to hedge against rising underlying prices is difficult