Mathematical Finance - meta - Maastricht University
Stochastic differential equations, the Ito integral, and the Ito formula. Diffusion and mean-reverting processes. Solution of the stochastic differential equations such as the geometric Brownian motion and Ornstein-Uhlenbeck processes.
Factors that affect option prices. Bounds for option prices. Put-call parity. Option valuation using binomial trees and lattices.
ST909: Continuous Time Finance for Interest Rate Models
The risk-neutral pricing measure for a binomial lattice and application to the valuation of equity options. Option valuation using the Black-Scholes model: risk-neutral pricing and equivalent martingale measure, complete markets, derivation of the Black-Scholes equation, including in Garman-Kohlhagen form, assumptions, pricing and hedging of simple derivatives contracts using the martingale approach, option valuation calculations using the Black-Scholes model.
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- ST Continuous Time Finance for Interest Rate Models.
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Equivalence of state-price deflator approach and risk-neutral pricing approach. The Greeks for an option: definitions, derivation and characteristics for European options, use in risk management of a portfolio of derivatives, including delta-hedging. Risk-neutral and state-price deflator approaches to the pricing of zero-coupon bonds and interest rate derivatives for a general single-factor diffusion model for the risk-free rate of interest. Vasicek, Cox-Ingersoll-Ross, and Hull-White single-factor models for the term structure of interest rates.
Calculating the price of zero coupon bonds with recovery rate. Modern Portfolio Theory and Investment Analysis.
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Option Pricing: Mathematical Models and Computation. Purpose of the Assessment: To demonstrate the extent to which students have assimilated material in the syllabus and can apply it to relevant problems and situations. The method of assessment is designed to comply with the requirements of the Institute and Faculty of Actuaries IFoA so that students who score sufficiently well in the examination at a level determined by the IFoA may gain professional exemption from CT8 of the professional examinations of the IFoA.
Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.
Course texts are provided by the library and there are no additional compulsory costs associated with the module. Undergraduate Postgraduate taught Postgraduate research Foundation Years Pre-sessional English language courses How to apply Clearing Free online learning Continuing professional development Prospectuses.
Module Overview Following an initial discussion of the assessment and measurement of investment risk, mean-variance portfolio theory is introduced and used to determine the risk and return for a portfolio of risky assets, the composition of the optimal such portfolio, and the location of the efficient frontier.
Use basic programing and simulation techniques, for instance, in derivative pricing and risk management. Hull J. Continuous-Time Finance. This chapter contains sections titled: Stochastic Processes and Filtrations. Classes of Processes Markov Processes. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username.
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