financial derivatives

The price of XYZ stock is currently at $100. After one period, the price will move to one of the following values: {$130,$80}. The risk-free asset returns $1.05 per $1 invested, at the end of the period. a) Find the risk-neutral probabilities governing the movement of XYZ s price. b) Find the state prices for each of the states. (Hint: The most general asset pricing model that applies to everything we do can be written as pt=Et[mt+1xt+1]. Price at time t,pt, is just a discounted expected future cash flow at t+1,xt+1, discounted by mt+1. We also examined contingent claims. We said that the prices of these claims at t, called state prices, depend on a particular state sS occurring at t+1 and are written as pc(s)pc(s) is the price at time t of a payoff of $1 at time t+1 only if state sS occurs at t+1. We deduced that the price at time t of an asset that pays x(s) at time t+1 in state sS can be written as price (x(s))=spc(s)x(s). How does the previous equation relate to pt=Et[mt+1xt+1] ?) c) Calculate the price of a $102-strike put using the state prices. The price of XYZ stock is currently at $100. After one period, the price will move to one of the following values: {$130,$80}. The risk-free asset returns $1.05 per $1 invested, at the end of the period. a) Find the risk-neutral probabilities governing the movement of XYZ s price. b) Find the state prices for each of the states. (Hint: The most general asset pricing model that applies to everything we do can be written as pt=Et[mt+1xt+1]. Price at time t,pt, is just a discounted expected future cash flow at t+1,xt+1, discounted by mt+1. We also examined contingent claims. We said that the prices of these claims at t, called state prices, depend on a particular state sS occurring at t+1 and are written as pc(s)pc(s) is the price at time t of a payoff of $1 at time t+1 only if state sS occurs at t+1. We deduced that the price at time t of an asset that pays x(s) at time t+1 in state sS can be written as price (x(s))=spc(s)x(s). How does the previous equation relate to pt=Et[mt+1xt+1] ?) c) Calculate the price of a $102-strike put using the state prices