Download A Course in Financial Calculus by Alison Etheridge PDF

By Alison Etheridge

This article is designed for first classes in monetary calculus aimed toward scholars with a very good historical past in arithmetic. Key options similar to martingales and alter of degree are brought within the discrete time framework, permitting an available account of Brownian movement and stochastic calculus. The Black-Scholes pricing formulation is first derived within the easiest monetary context. next chapters are dedicated to expanding the monetary sophistication of the types and tools. the ultimate bankruptcy introduces extra complicated subject matters together with inventory rate versions with jumps, and stochastic volatility. a number of workouts and examples illustrate how the tools and ideas will be utilized to lifelike monetary questions.

Show description

Read or Download A Course in Financial Calculus PDF

Best investments & securities books

Black-Scholes and beyond: Option pricing models

An exceptional publication on alternative pricing! For the 1st time, the fundamentals on glossy choice pricing are defined ``from scratch'' utilizing in simple terms minimum arithmetic. industry practitioners and scholars alike will find out how and why the Black-Scholes equation works, and what different new tools were built that construct at the luck of Black-Shcoles.

A Course in Financial Calculus

This article is designed for first classes in monetary calculus geared toward scholars with a superb historical past in arithmetic. Key innovations similar to martingales and alter of degree are brought within the discrete time framework, permitting an obtainable account of Brownian movement and stochastic calculus. The Black-Scholes pricing formulation is first derived within the least difficult monetary context.

Handbook of Fixed-Income Securities

A complete advisor to the present theories and methodologies intrinsic to fixed-income securities Written via recognized specialists from a cross-section of academia and finance, guide of Fixed-Income Securities incorporates a compilation of the main up to date fixed-income securities options and strategies.

Additional info for A Course in Financial Calculus

Sample text

For example, suppose I play a game with a friend in which each play is equivalent to flipping a fair coin. If it comes up heads I pay her a dollar, otherwise she pays me a dollar. For each n, Sn models my net gain after n plays. Recall from Exercise 13 of Chapter 2 that E[Sn ] = 0 and var(Sn ) = n. 1 and cov(Sn , Sm ) = n ∧ m. 7 that {Sn }n≥0 is a P-martingale. It remains to calculate the covariance. cov(Sn , Sm ) = E[Sn Sm ] − E[Sn ]E[Sm ] = E [E[Sn Sm |Fm∧n ]] = E [Sm∧n E [Sm∨n |Fm∧n ]] = 2 ] E[Sm∧n = var(Sm∧n ) = m ∧ n.

5, converges to a limit, Y∞ as n → ∞. Show that E [Yn ] = 1 for all n, but that Y∞ = 0. Why does this not contradict the conclusion of the Optional Stopping Theorem? 50 trees and martingales 16 Recall Jensen’s inequality: if g is a convex function and X a real-valued random variable then E [g(X )] ≥ g (E [X ]) . 7) of the discounted price of an American call option on non-dividend-paying stock as the smallest Qsupermartingale that dominates {e−r nδt (Sn − K )+ }n≥0 to prove that the price of an American call on non-dividend-paying stock is the same as that of a European call with the same strike and maturity.

Once again our financial market will consist of just two instruments, the stock and a cash bond. As before we assume that unlimited amounts of both can be bought and sold without transaction costs. There is no risk of default on a promise and the market is prepared to buy and sell a security for the same price (that is, there is no bid–offer spread). 1 S3 The tree of stock prices. We suppose the market to be observable at times 0 = t0 < t1 < · · · < t N = T . The stock Over each time period [ti , ti+1 ] the stock follows the binary model.

Download PDF sample

Rated 4.43 of 5 – based on 9 votes