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

Ask Question & Get Answers from Experts
Browse some more (Finance Basics) Materials
CalculateĀ the financial ratios for the assigned company's financial statements, and then interpret those results against company historical data as well as industry benchmar
During 2014, Eagle Beach Company EBC) had sales of $1,000,000, cost of goods sold of $600,000, administrative and selling expenses of $95,000, depreciation expense of $140,000
Scenario: The president of Party Plates has requested a new proposal from your team. She would like information on wireless technologies and how they might be used in your o
What is the cross-rate of euros to Swiss francs (Euro/SF)? Enter your answer rounded off to FOUR decimal points - how many yen could one U.S. dollar buy tomorrow? Enter your a
A mutual fund declares that the salaries of its fund managers will depend on the performance of the fund. If the fund loses money, the salaries will be zero.
According to Gorton; The limited liability of shareholders in a business creates moral hazard because owners can take risks that can benefit them at the potential expense of c
A Company has fixed operating expenses of $25,000, a per unit sales price of $5, and a variable cost per unit of $3. What is its operating breakeven point if it desires net op
Assume you own stock in a corporation. The current price is $25. Another corporation has just announced that it wants to buy your company and will pay $35 per share to acquire