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4. Suppose the functions 4,0 : [0,T X R R and § : R ...

4. Suppose the functions 4,0 : [0,T X R R and § : R R are given and we are trying to find a function F : [0,T] X R R which satisfies the following boundary value problem: (*) a) Show that if F(t,x) solves the above problem, then the function G(t,x) e-r(T-t) x) solves the problem: (#)...

1. Prove by mathematical induction: E/- - a) For every in...

1. Prove by mathematical induction: E/- - a) For every integer b) For every integer &amp; , c) For every integer positive, negative, or zero, 2. notes to Use the information in the class find 3. Let there be only two goods X and Y and let X and y be quantities of the two goods pur...

(1) The prices of three put options with strikes 40, 50, and...

(1) The prices of three put options with strikes 40, 50, and 70, but otherwise identical, are $10, $20, and $30, respectively. (i) Show that the upward convexity of the price of the put with respect to the strike price is violated in this case; (ii) Find an arbitrage opportunity. (2) Show that ...

1.4 Consider the time series Xt = Bo + B1t + Wt, where Bo ...

1.4 Consider the time series Xt = Bo + B1t + Wt, where Bo and B1 are regression coefficients, and Wt is a white noise process with variance of (a) Determine whether Xt is stationary. (b) Show that the process Yt = Xt - Xt-1 is stationary. (c) Show that the mean of the moving average = 1 is 8...

(3) Let $2.26 be the price of a European call option with st...

(3) Let $2.26 be the price of a European call option with strike $35 and expiration in 3 months; and let its delta be 0.56 and its gamma be 0.08. The current stock price is $35, volatility of the stock is 25%, and the annual continuously compounded interest rate is 3%. (i) (? points) Find the t...

Question 1. Stochastic integration: A small company is inve...

Question 1. Stochastic integration: A small company is investing resources in a risky project that it hopes will be profitable. The project could, for example, represent the manufacturing and selling of a gadget in a local market. The performance of the market is measured by the Brownian motion ...

2 Extra credit: Simulating a life-cycle portfolio choice st...

2 Extra credit: Simulating a life-cycle portfolio choice strategy Here is an optional (but fun!) exercise to give you a flavor for the types of things that you can accomplish with monte carlo simulations. It turns out that a few lines of code can provide a pretty realistic picture of the po...

Answer the following questions making sure to clearly explai...

Answer the following questions making sure to clearly explain the procedure you followed to determine your answers. 1. Plot the term structure of Treasury rates on February 15, 2011 for maturities up to 30 years. 2. Compute the monthly compounded 1-month Treasury rate on February 15, 2011. 3. Com...

Part a) Ordinary Differential Equation Application ODEs, in...

Part a) Ordinary Differential Equation Application ODEs, investments and interest rates: In a period of falling interest rates, the (continuously compounded) short interest rate as a function of t is 1 per annum. (a) What is the value at t = 0 of a contract that makes a payment at time t = 10 o...

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