+1-415-670-9189
info@expertsmind.com
Calculate the price of the european call option
Course:- Finance Basics
Reference No.:- EM132231819




Assignment Help
Expertsmind Rated 4.9 / 5 based on 47215 reviews.
Review Site
Assignment Help >> Finance Basics

Problem set

1. Option Pricing via FFT Techniques: The Heston Model is defined by the following system of stochastic differential equations:

dSt = rStdt + √νt StdWt1
t = κ(θ - νt) dt + σ√νt dWt2
Cov(dWt1, dWt2) = ρ dt

The characteristic function for the Heston Model is known to be:

ω(u) = (exp (iu ln S0 + iu(r - q)t + κθt(κ-iρσu)/σ2)/(cosh λt/2 + (κ-iρσu)/λ.sinh λt/2)2κθ/σ2      (1)

Φ(u) = ω(u) (exp -(u2 + iu)ν0/λ coth λt/2 + κ - iρσu) (2)

λ = √(σ2(u2 + iu) + (κ - iρσu)2) (3)

Assume the risk-free rate is 2%, the initial asset price is 250 and that the asset pays no dividends.

(a) Exploring FFT Technique Parameters Consider a European Call Option with strike 250 expiring in six months.

Additionally, assume you know that the parameters of the Heston Model are:

σ = 0.2

ν0 = 0.08

κ = 0.7

ρ = -0.4

θ = 0.1

i. Calculate the price of the European Call option with many values for the damping factor, α. What values of α seem to lead to the most stable price?

ii. Using the results above, choose a reasonable value of α and calculate the price of the same European Call with various values of N and Δk (or equivalently N and B). Comment on what values seem to lead to the most accurate prices, and the efficiency of each parameterization.

iii. Calculate the price of a European Call with strike 260 using various values of N and Δk (or N and B). Do the same sets of values for N , B and Δk produce the best results? Comment on any differences that arise.

(b) Exploring Heston Parameters Assume the risk-free rate is 2.5%, the initial asset price is 150 and that the asset pays no dividends.

σ = 0.4
ν0 = 0.09
κ = 0.5
ρ = 0.25
θ = 0.12

i. Using these parameters, calculate Heston Model prices for three-month options at a range of strikes and extract the implied volatilities for each strike. Plot the implied volatility σ(K) as a function of strike.

ii. Use the FFT pricing technique to obtain prices of 150 strike calls at many expiries. Extract the implied volatility for each and plot the term structure of volatility by plotting time to expiry on the x-axis and implied volatility on the y-axis.

iii. Holding all other parameters constant, vary each of the model parameters and plot the updated volatility skews and term structures. Comment on the impact that each parameter has on the skew and term structure.




Put your comment
 
Minimize


Ask Question & Get Answers from Experts
Browse some more (Finance Basics) Materials
Franklin Templeton has just invested $9, 260 for his son (age one). This money will be used for his son's education 18 years from now. He calculates that he will need $71,23
How might the British and American T-bill and foreign exchange markets adjust to this situation? Present and discuss an equilibrium consistent with the concept of interest r
The submission should include a detailed review of the most recent available Annual Report and will use key financial ratios (important) to analyse the financial statements
Foreign Currency Derivatives Please also add a little more information about Singapore dollar vs Australian dollar in order to make it attractive, such as current exchange rat
Ryngaert Inc. recently issued noncallable bonds that mature in 15 years. They have a par value of $1,000 and an annual coupon of 5.7%. If the current market interest rate is
If the plant has projected net income of $1,735,000, $2,105,000, $1,954,000, and $1,286,000 over these four years, what is the project's average accounting return (AAR)?
A ski resort plans to eventually add 5-new chairlifts. One lift costs $2 million, making slope costs another $1.3 million. The lift allows 300 additional skiers, but there are
What are risks associated with Walmart's equity financing decisions? Provide a minimum of three associated risks. How would you evaluate the financing decisions made by Walmar