Stochastic Calculus Paris Dauphine University - Master IEF (272)
Stochastic Calculus. Paris Dauphine ... Exercise 4 Consider a financial market with a money account, a stock, and an European call option on the stock with ...
Stochastic Calculus Paris Dauphine University - Master IEF (272) Jérôme MATHIS (LEDa) Exercises Chapter 1
Exercise 1 There are two periods, t 2 f0; 1g. There are two assets. One non-risky asset (money that can be borrowed or lend) that returns r = 14 at time 1. And one risky asset which is a stock of price S0 = 4 at time 0. At date 1, a coin is tossed. ( 8 if Head The price of the stock at time 1 is S1 = . 2 if Tail Assume our initial wealth is (money) x = 1:2e and we want to buy at time 0, of the stock.
0
=
1 2
shares
(a) How much do we have to borrow? (b) What is our in debt, It , to the money market, at time t 2 f0; 1g? (c) What is our stock value,
0 St ,
at time t 2 f0; 1g?
(d) What is our portfolio value, Xt , at time t 2 f0; 1g? (e) At time 1, what is the value of an European call option with underlying asset S and strike K = 5? (f) Compare the result of (d) with the one obtained in (e). (g) Under NAO, what is the value of our European call option at time 0?
Exercise 2 Consider Exercise 1. Suppose the price of the option at time 0 is 1:21e. Construct an arbitrage portfolio that uses one unit of the option.
Exercise 3 Consider Exercise 1. Suppose the price of the option at time 0 is 1:19e. Construct an arbitrage portfolio that uses one unit of the option.
Exercise 4 Consider a …nancial market with a money account, a stock, and an European call option on the stock with strike price K = 98. Suppose at time t = 0, the stock price is S0 = 100 and the price at time t = 1 is either 1
S1 (H) = 112 or S1 (T ) = 84. Suppose the interest rate on the money account is r = 5%. We want to obtain a no-arbitrage price for the call option. The following table lists the payo¤ structure of the …nancial market. t=0 t = 1; T t = 1; H Money 1 1:05 1:05 Stock 100 84 112 + Option ? (84 98) = 0 (112 98)+ = 14 Under NAO, what is the price of the option at time t = 0?
Exercise 5 Suppose the price of the option in Exercise 4 is 5e. Construct the arbitrage that uses one unit of the option.
Exercise 6 Suppose the price of the option in Exercise 4 is 15e. Construct the arbitrage that uses one unit of the option.
Stochastic Calculus. Paris Dauphine ... A financial institution has just announced that it will trade a derivative that pays off an euro amount equal to lnST at time T ...
Exercise 2 A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is ...
Stochastic Calculus. Paris Dauphine University ... At date t = 0, a financial institution issues two derivatives that each matures at time t = 2. According to the ...
The stock price is $47 and the strike price is $50. ... Exercise 2 An investor sells a European call option with strike price of K and maturity T ... Exercise 5 Describe the terminal value of the following portfolio : a newly entered-into long ... Sh
Exercise 1 (Done) Companies A and B have been offered the following rates per ... at the current exchange rate. The companies have been quoted the following ...
Exercise 1 An investor enters into a short forward contract to sell 100,000 British pounds ... Exercise 3 Suppose that you write a put contract with a strike price of $40 and an expiration ... sell 10 million Japanese yen on next year January 1.
Exercises Chapter 2. Exercise 1 ... Exercise 2 What does a limit order to sell at $2 mean? ... Exercise 9 Suppose that on October 24 (current year), a company sells one April (next year) ... It closes out its position on January 21 (next year).
Exercise 1 Call options on a stock are available with strike prices of $15, $171. 2. , and $20 and expiration dates in three months. Their prices are $4, $2, and $1.
Exercise 5 The six-month and one-year zero rates are both 10% per annum. ... enables the holder to earn 9.5% for a three-month period starting in one year on a ...
You are managing a bond portfolio worth $6 million. The ... (Assume no difference between forward andfutures rates for the purposes of your calculations.) 1 ...
Exercise 1 What is a lower boundfor the price of a four-month call option on a non-dividend- paying stock when the stock price is $28, the strike price is $25, and ...
paying stock when the stock price is $30 and the risk-free interest rate (with ... Exercise 4 The risk-free rate of interest is 7% per annum with continuous ...
Exercise 2 (Done) A company has a $20 million portfolio with a beta of 1.2. ... Exercise 4 (Done) On July 1, an investor holds 50,000 shares of a certain stock.
Stochastic Calculus ... On financial markets, there exist practitioners called arbitrageurs ... In quantitative finance, we assume that arbitrage opportunities do.
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4 avr. 1991 - Etudiante en Master 2 de Marketing et Stratégie, je recherche un stage de fin ... Lettres, Mathématiques, Sciences sociales et Culture générale.
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