Mathematics of Finance and Valuation
- introduce the main mathematical ideas involved in the modelling of asset price evolution and the valuation of contingent claims (such as call and put options) in a discrete and in a continuous framework
- Explain the basic financial derivative contracts, how and when they are used
- price contingent claims in the model with one risky asset and two random outcomes (states).
- price contingent claims in the model with several risky assets and one period of time.
- explain the concept of a complete financial market and the absence of arbitrage in the one-period model.
- price contingent claims in the model with one risky asset and two random outcomes (states)
- explain the concept of a complete financial market and the absence of arbitrage in a multi-period model
- Apply the required concepts from the theory of random sequences: filtration, adapted and predictable sequences, conditional expectation, martingales, martingale measures.
- apply the general results of the multiperiod model in the binomial model
- explicitly compute the equivalent martingale measure in the binomial model
- explain the concept of a random process, and, in particular, the Brownian motion and the geometric Brownian motion
- apply basic rules of the Ito calculus for stochastic processes
- to apply the Black-Schles formula for European options
- compute implied volatility
- price perpetual American put options in the Black-Scholes model
- Financial environment1.1 Present value of future income 1.2 Bonds, stocks, derivative securities 1.3 Arbitrage arguments 1.4 Hedging
- One risky asses and two states2.1 The simplest market model 2.2 Valuation of forward and futures contracts 2.3 Valuation of options 2.4 Valuation by expectation
- One period many assets3.1 Description of the model 3.2 The notion of arbitrage 3.3 Fundamental Theorem, of Asset Pricing
- Multi-period models4.1 Information trees and related notions 4.2 Valuation of contracts in the multiperiod models 4.3 Arbitrage in the multiperiod model 4.4 Risk-neutral measures
- The binomial model5.1 The T-period binomial model 5.2 Valuation of different contracts
- Continuous-time modelling6.1 The discrete random walk and Brownian motion 6.2 Stochastic differential equations 6.3 Itô’s formula
- Black-Scholes model7.1 Geometric Brownian motion as a stock price model 7.2 The Black-Scholes equation 7.3 The Black-Scholes formula for option prices
- Perpetual options8.1 The notion of a perpetual option 8.2 The Cauchy-Euler equation and the value of a perpetual option
- home assignments
- UoL examUoL exam is not counted in overall grade
- October test
- class activities
- Interim assessment (2 module)0.29 * home assignments + 0.01 * class activities + 0.5 * examination + 0.2 * October test
- Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007
- Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004
- Stochastic calculus for finance. Vol.2: Continuous-time models, Shreve, S. E., 2004