The movement of a share price over the next two months is to be modelled using...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The movement of a share price over the next two months is to be modelled using a two-period recombining binomial model. Over each month, it is assumed that the share price will either increase or decrease by 10%. (1) Over each month, the risk-neutral probability of an up-step is q=0.55. Calculate the monthly risk-free force of interest r that has been used to arrive at this figure. [1] (ii) The current share price is 1. The annualised expected force of return on the share is = 30%. Calculate the state-price deflators in each of the three possible final states of the share price. (iii) Calculate the value of each of the following two-month derivatives: (a) a derivative with payoff profile (1,0,0) (b) a derivative with payoff profile (0.1,0) (c) a derivative with payoff profile (0,0,1) (d) a European call option with a strike price of K = 0.95 (e) a European put option with a strike price of K=1.05 (f) a derivative whose payoff is 2x|5-0.98, where S is the share price at the end of the two months. [5] (1) (ii) (ii) Let X, be a diffusion that satisfies X, (X,,t)dt o (X₁.) dB, where B, is a standard Brownian motion. Let f(x, t) be a function of r and X₁. By considering Taylor's theorem, suggest a partial differential equation that must be satisfied by /(X.) in order that it is a martingale. [3] Verify that your equation holds when f(x,1)=B² -1. Find g (1) such that B, +g (1) B, is a martingale [1] E [2] [Total 6] In the following. B, denotes a standard Brownian motion. (i) Write down the general solution of the stochastic differential equation: dX, =-yX,dt + odB, (ii) Hence determine the solution of the stochastic differential equation: dR, = 0.8 (4-R,)dt +dB, where Ro = 5. Find the distribution of the process R, at times and in the long-term. [1] [1] 3 [3] [Total 5] The movement of a share price over the next two months is to be modelled using a two-period recombining binomial model. Over each month, it is assumed that the share price will either increase or decrease by 10%. (1) Over each month, the risk-neutral probability of an up-step is q=0.55. Calculate the monthly risk-free force of interest r that has been used to arrive at this figure. [1] (ii) The current share price is 1. The annualised expected force of return on the share is = 30%. Calculate the state-price deflators in each of the three possible final states of the share price. (iii) Calculate the value of each of the following two-month derivatives: (a) a derivative with payoff profile (1,0,0) (b) a derivative with payoff profile (0.1,0) (c) a derivative with payoff profile (0,0,1) (d) a European call option with a strike price of K = 0.95 (e) a European put option with a strike price of K=1.05 (f) a derivative whose payoff is 2x|5-0.98, where S is the share price at the end of the two months. [5] (1) (ii) (ii) Let X, be a diffusion that satisfies X, (X,,t)dt o (X₁.) dB, where B, is a standard Brownian motion. Let f(x, t) be a function of r and X₁. By considering Taylor's theorem, suggest a partial differential equation that must be satisfied by /(X.) in order that it is a martingale. [3] Verify that your equation holds when f(x,1)=B² -1. Find g (1) such that B, +g (1) B, is a martingale [1] E [2] [Total 6] In the following. B, denotes a standard Brownian motion. (i) Write down the general solution of the stochastic differential equation: dX, =-yX,dt + odB, (ii) Hence determine the solution of the stochastic differential equation: dR, = 0.8 (4-R,)dt +dB, where Ro = 5. Find the distribution of the process R, at times and in the long-term. [1] [1] 3 [3] [Total 5]
Expert Answer:
Answer rating: 100% (QA)
Binomial Model and RiskNeutral Pricing Part 1 I RiskNeutral Probability and Force of Interest In a twoperiod binomial model with an upmovement probabi... View the full answer
Related Book For
Posted Date:
Students also viewed these finance questions
-
A stock price is currently $40. It is known that at the end of 1 month it will be either $44 or $36. The risk-free interest rate is 6% per annum with continuous compounding. What is the value of a...
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
How would you apply this concepts to call center statistics? There are two numerical ways of describing quantitative variables, namely measures of location, and measures of dispersion. Measures of...
-
A 750-lb space vehicle traveling with a velocity v0 = (1500 ft/s)k passes through the origin O. Explosive charges then separate the vehicle into three parts A, B and C, weighing, respectively, 125lb,...
-
Statistical Research Service, Inc. (SRSI) ended 2008 with retained earnings of \(\$ 75,000\). During 2009 SRSI earned net income of \(\$ 90,000\) and declared dividends of \(\$ 30,000\). Also during...
-
Go to the Web site for the Malcolm Baldrige National Quality Award and find the questionnaire titled "Are We Making Progress?" a. Download the questionnaire and answer the questions relative to your...
-
On April 15, 2010, Powell, Inc., obtained a six-month working capital loan from its bank. The face amount of the note signed by the treasurer was $300,000. The interest rate charged by the bank was...
-
According to Unilever s management, _ _ _ _ _ _ _ _ _ _ _ _ . Select answer from the options below it is impossible to increase sales without also increasing its environmental footprint. a company...
-
In Part III (Appendix 11B) of the audit case, the audit staff of Adams, Barnes & Co. identified specific revenue risks on working paper RA-12 (page 494). However, the Summary of Audit Approach...
-
On January 1, 2022, Demi Lee and Quinn Brown formed The Custom Cabinets Company. Demi contributed cash of $240,000 to the partnership in return for a 60% interest in capital and profits. Quinn...
-
solve areas in yellow. Both labor variance and parts variance should equal 80,025 MRO Department - 2020 Results Change in Gross Margin 80,025 Revenues (billed out): Budget Actual Fav./(Unfav.) -...
-
A bond has a par value of $1,000, pays $70 semiannually and has a maturity of 15 years. 1) If the bond earns 12% per year, what is the price of the bond? Rate Nper PMT FV Type PV 2) What is the yield...
-
Calculate the Cash Flow balance (as per balance sheet) in year 3. Assume all missing data is zero Year 1 Year 2 Year 3 P&L Revenues 200.0 250.0 300.1 COGS (75.0) (90.0) (105.0) OPEX (12.0) (15.0)...
-
3 Walking Bear Resources Inc. Equity Section of the Balance Sheet March 31, 2023 Contributed capital: Preferred shares, $17 cumulative, 2,900 shares authorized, issued, and outstanding 812,000...
-
Apply Slack and Lewis (S/L) Operations Strategy (OS) framework and Matrix to a real-world company of your choice. The following structure is recommended. Introduce the organisation and the state of...
-
Discuss medial temporal lobe amnesia, emphasizing the cases of H.M. and R.B. What have we learned from the study of this disorder? Compare the following three theories of cerebral asymmetry: the...
-
Describe basic managerial approaches to implementing controls and how these are implemented.
-
A total of 46 percent of the voters in a certain city classify themselves as Independents, whereas 30 percent classify themselves as Liberals and 24 percent say that they are Conservatives. In a...
-
In the text, we noted that when the Xi are all nonnegative random variables. Since an integral is a limit of sums, one might expect that whenever X(t), 0 t Define, for each nonnegative t, the random...
-
Use the conditional variance formula to determine the variance of a geometric random variable X having parameter p.
-
Taylor Company reports free cash flow of \(\$ 15,000\), total cash of \(\$ 18,000\), net income of \(\$ 50,000\), current assets of \(\$ 90,000\), average current liabilities of \(\$ 38,400\), and...
-
Which of the following is not a cash equivalent? a. Short-term U.S. Treasury bill b. Short-term certificate of deposit c. Money-market account d. IBM common stock
-
Smith \& Sons reports interest expense of \(\$ 90,000\) on its income statement. The beginning and ending balances for interest payable reported on its balance sheet are \(\$ 15,000\) and \(\$...
Study smarter with the SolutionInn App