The value of a share per unit develops according to a geometric Brownian motion with drift given

Question:

The value of a share per unit develops according to a geometric Brownian motion with drift given by

\[X(t)=10 e^{0.2 t+0.1 S(t)}, t \geq 0\]

where $\{S(t), t \geq 0\}$ is the standardized Brownian motion. An investor owns a European call option with running time $\tau=1$ [year] and with strike price

\[x_{s}=\$ 12\]

on a unit of this share.

(1) Given a discount rate of $\alpha=0.04$, determine the mean discounted profit of the holder of the option.

(2) For what value of the drift parameter $\mu$ do you get the fair price of the option?

(3) Determine this fair price.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

See More Books

Question Posted: Apr 26, 2024 04:01 PM

See More Questions

1 What are the main components of personal financial planning? Solve What is the purpose of a financial plan? Solve Identify some common actions taken to achieve financial goals. How does a job...
13. What is a lower bound for the price of 3-month call option on a non- dividend-paying stock when the stock price is $50, the strike price is $45, and the 3-month risk-free interest rate is 8%?...
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
A space-filling curve is a continuous curve in the unit square that passes through every point. Write a recursive Turt le client that produces these recursive patterns, which approach a space-filling...
Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current...
Outdoor Living specializes in outdoor furniture and spas. Owner Cheryl Homberg is expanding the store. She is deciding which product line to emphasize. To make this decision, she assembles the...
Distinguish among totalitarianism, socialism, and democracy. What are the implications of each for internationalizing firms? LO.1
The manager of Collins Import Autos believes the number of cars sold in a day (Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working...
Please help and show work. Thank you! As a part of an employment interview, you are given the partial income statement and selected financial ratios shown for Sneaky Pete's, a chain of western...
The random price $X(t)$ of a risky security per unit at time $t$ is \[X(t)=5 e^{-0.01 t+B(t)+0.2|B(t)|}\] where $\{B(t), t \geq 0\}$ is the Brownian motion with volatility \[\sigma=0.04\] At...
The value (in $\$$ ) of a share per unit develops, apart from the constant factor 10 , according to a geometric Brownian motion $\{X(t), t \geq 0\}$ given by \[X(t)=10 e^{B(t)}, 0 \leq t \leq...
What problems do you see for MNEs that must bargain with unions in multiple countries? How would you advise those problems be resolved? Ford Motor Company manufactures cars, trucks, and parts in 30...
n1 = 15, n2 = 18, S = 280, H1: m1 > m2. Exercises 57 present sample sizes and the sum of ranks for the rank-sum test. Compute S, S, and the value of the test statistic z. Then find the P-value.
n1 = 25, n2 = 32, S = 850, H1: m1 m2. Exercises 57 present sample sizes and the sum of ranks for the rank-sum test. Compute S, S, and the value of the test statistic z. Then find the P-value.
Evaluate the matrix element $\left\langle j_{1} j_{2} J\left|T_{k q}(1) ight| j_{1}^{\prime} j_{2}^{\prime} J^{\prime} ightangle$, where the tensor operator $T_{k q}(1)$ operates only on the part of...
Mark Gold opened Gold Roofing Service on April 1. Transactions for April are as follows: 1 Gold contributed $\$ 15,000$ of his personal funds in exchange for common stock to begin the business. 2...
n1 = 20, n2 = 30, S = 400, H1: m1 < m2. Exercises 57 present sample sizes and the sum of ranks for the rank-sum test. Compute S, S, and the value of the test statistic z. Then find the P-value.
Azure Corporation had the following 2011 income statement data: The following accounts increased during 2011 by the amounts shown: Accounts Receivable, $17,000; Inventory, $11,000; Accounts Payable,...
Place a tick in the appropriate grid to identify the balance that would be brought down in each of the following named accounts, in the books of Rizwy Mohamed: (a) In the Cash account: if Rizwy...
Indicate whether the following managerial policy increases the risk of a death spiral:Use of low operating leverage for productionGroup of answer choicesTrueFalse
It is typically inappropriate to include the costs of excess capacity in product prices; instead, it should be written off directly to an expense account.Group of answer choicesTrueFalse
Firms can avoid the death spiral by excluding excess capacity from their activity bases. Group of answer choicesTrueFalse

The value of a share per unit develops according to a geometric Brownian motion with drift given

Question:

Step by Step Answer:

Data from Example 117 A European call option ...View the full answer

Applied Probability And Stochastic Processes

Students also viewed these Business questions