We consider a (European) call option on a stock with expiration in 3 months and strikeprice $10. The annual interest rate on the market is r = 4%. The current price of the stockis $10 and we assume that the stock follows a geometric Brownian motion (Black-Scholes)model with parameters = 6% and σ = 0.2.(a) Determine the price Fo of this option at time t=: 0 (today).(b) Using the formulas provided in the lecture videos, calculate the value of each of theGreeks for this option. Namely, calculate A, T, v, О, p.(c) Find a formula for the change of the option price with respect to a change in theaf (St, t)Әкstrike price. In other words, determine(d) For each of the suggested modifications below, use an approximation to determinethe change in the price of the option above without actually recalculating the price.For each one, provide an intuitive argument to explain why the price increases ordecreases.(i) The rate of return μ decreases to 5%.(ii) The interest rate r decreases to 3%.(iii) The volatility decreases to σ = 0.1.(iv) The expiration date changes to 4 months.(v) The strike price goes up to $11.(vi) The current stock price drops instantaneously to $9.

Summary TableGreekValuePrice F00.448Delta Δ0.5596Gamma Γ0.3965Vega ν1.9825Theta Θ-0.6023Rho…

Answered: We consider a (European) call option on…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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