1. Consider a market with one stock and one money market account, with the same assumptions on parameters (such as r, μ and σ²) 02) as in the derivation of the Black-Scholes formula given in class for European call option. Consider a contingent claim whose payoff depends on two dates T₁ and T2, with T₂ > T₁ > 0 and two numbers K₁ > 0 and K₂ > 0. The buyer of this contingent claim has the right to buy 1 share of the stock at time T₁ at price K₁. If the price of the stock at time T₁ is lower than or equal to K1, she then has a right to by the stock at price K2 at time T2. (She does not have the buying opportunity at time T2 if the price of the stock at time T₁ is strictly larger than K₁.) Find a formula for the current price (i.e. at time t = 0) of this contingent claim. The formula has to be explicit in the sense that one could feed into a computer program just like the Black-Scholes formula. The formula may contain integrals. It is not necessary to simplify the formula.

A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million, whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high. The payoff table depicting revenues and is shown in the following table. payoffs (PV in millions) states of nature Low Option Moderate high Small 10 10 10 Medium 7 12 12 Large -4 2 16 (a) Which alternative should the manager…

The table here shows the no-arbitrage prices of securities A and B that we calculated.Cash Flow in One YearSecurity Market Price Today Weak Economy Strong EconomySecurity A 231 0 600Security B 346 600 0a. What are the payoffs of a portfolio of one share of security A and one share of security B?b. What is the market price of this portfolio? What expected return will you earn from holdingthis portfolio?

A company is considering a project which has three options. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature. For a medium facility, low demand will have a present value of $7 million,whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high.The payoff table depicting revenues and is shown in the following table.  (a) Which alternative should the manager choose under the maximax criterion? (b) Which option should the manager choose under the maximin criterion? (c) Which…