Reference no: EM131243660
The squared payout A derivative contract has payout at maturity defined by D(T, T) = 
, and priceD(t, T) at current time t.
(a) One trader states that the replicating portfolio for this derivative is a holding of St stocks, and thus D(t, T) = 
. What is wrong with this argument?
(b) Another trader states that the replicating portfolio is a holding of ST stocks, and thus D(t, T) = StST. What is wrong with this argument?
(c) Suppose the risk-neutral distribution of ST conditional on St, with respect to the money market numeraire, is lognormal (log St + ν(T - t), σ2(T - t)), that is, log ST | St ∼ N(log St + ν(T - t), σ2(T - t)). Use a martingale condition for ST/MT to find ν in terms of σ and r, the constant, continuously compounded interest rate.
(d) Use the fundamental theorem to write down, but do not solve, an integral expression for D(t, T) involving a normal probability density function.
(e) Suppose you are also told that the risk-neutral distribution of ST conditional on St, with respect to the stock numeraire, is lognormal (log St + γ (T - t), σ2(T - t)). Use an appropriate martingale condition, and the fact that 1/ST is also lognormal, to find γ in terms of r and σ.
(f) Hence use the fundamental theorem to prove that, assuming the distribution in (e) holds,
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