Question

You are given the following Black-Scholes-Merton formula for pricing a European put option on a non-dividend-paying stock: p = Ke^{-rT}?(-d_2) - S_0?(-d_1), where d_1 = frac{ln(frac{S_0}{K})+(r+frac{sigma^2}{2})T}{sigmasqrt{T}}, d_2 = d_1 - sigmasqrt{T}, and ?() is the cumulative distribution function of standard Normal distribution. (a) Briefly discuss the assumptions behind the Black-Scholes-Merton formula. (b) Discuss the meanings of the Greeks ?, ?, and ?, and determine the signs of ? and ? for the European put option. (c) Suppose that an investor currently holds a portfolio of derivatives on the underlying stock, which has ? = -500, ? = -2000, and ? = 1000. A traded option is available on the market with ?_c = 0.5, ?_c = 1.5, and ?_c = 0.5, as well as another one with ?_c = -0.25, ?_c = 1, and ?_c = 0.75. If the investor wants to neutralize all the three Greeks, what would be her position on the two traded options and on the underlying stock?

          You are given the following Black-Scholes-Merton formula for pricing a European put option on a non-dividend-paying stock:

p = Ke^{-rT}?(-d_2) - S_0?(-d_1),

where d_1 = frac{ln(frac{S_0}{K})+(r+frac{sigma^2}{2})T}{sigmasqrt{T}}, d_2 = d_1 - sigmasqrt{T}, and ?() is the cumulative distribution function of standard Normal distribution.

(a) Briefly discuss the assumptions behind the Black-Scholes-Merton formula.

(b) Discuss the meanings of the Greeks ?, ?, and ?, and determine the signs of ? and ? for the European put option.

(c) Suppose that an investor currently holds a portfolio of derivatives on the underlying stock, which has ? = -500, ? = -2000, and ? = 1000. A traded option is available on the market with ?_c = 0.5, ?_c = 1.5, and ?_c = 0.5, as well as another one with ?_c = -0.25, ?_c = 1, and ?_c = 0.75. If the investor wants to neutralize all the three Greeks, what would be her position on the two traded options and on the underlying stock?

$You are given the following Black-Scholes-Merton formula for pricing a European put option on a non-dividend-paying stock: p = Ke^-rT?(-d2) - S0?(-d1), where d1 = fracln(fracS0K)+(r+fracsigma^22)TsigmasqrtT, d2 = d1 - sigmasqrtT, and ?() is the cumulative distribution function of standard Normal distribution. (a) Briefly discuss the assumptions behind the Black-Scholes-Merton formula. (b) Discuss the meanings of the Greeks ?, ?, and ?, and determine the signs of ? and ? for the European put option. (c) Suppose that an investor currently holds a portfolio of derivatives on the underlying stock, which has ? = -500, ? = -2000, and ? = 1000. A traded option is available on the market with ?c = 0.5, ?c = 1.5, and ?c = 0.5, as well as another one with ?c = -0.25, ?c = 1, and ?c = 0.75. If the investor wants to neutralize all the three Greeks, what would be her position on the two traded options and on the underlying stock?$

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