An Introduction to the Mathematics of Financial DerivativesAn Introduction to the Mathematics of Financial Derivatives is a popular, intuitive text that eases the transition between basic summaries of financial engineering to more advanced treatments using stochastic calculus. Requiring only a basic knowledge of calculus and probability, it takes readers on a tour of advanced financial engineering. This classic title has been revised by Ali Hirsa, who accentuates its wellknown strengths while introducing new subjects, updating others, and bringing new continuity to the whole. Popular with readers because it emphasizes intuition and common sense, An Introduction to the Mathematics of Financial Derivatives remains the only "introductory" text that can appeal to people outside the mathematics and physics communities as it explains the hows and whys of practical finance problems. Facilitates readers' understanding of underlying mathematical and theoretical models by presenting a mixture of theory and applications with handson learning. Presented intuitively, breaking up complex mathematics concepts into easily understood notions. Encourages use of discrete chapters as complementary readings on different topics, offering flexibility in learning and teaching. 
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This is a great text. Take it slow in the beginning while reading and make sure everything is clear to you. Everything builds very logically. A great educational tool.
Contents
Financial Derivatives A Brief Introduction  1 
A Primer on the Arbitrage Theorum  13 
Calculus in Deterministic and Stochastic Environments  45 
Pricing Derivatives Models and Notation  77 
Tools in Probability Theory  91 
Martingales and Martingale Representations  119 
Differentation in Stochastic Environments  156 
The Weiner Process and Rare Events in Financial Markets  173 
The BlackScholes PDE  296 
Pricing Derivative Products  312 
Equivalent Martingale Measures  345 
New Results and Tools for InterestSensitive Securities  368 
Arbitrage Theorem in a New Setting Normalization and Random Interest Rates  379 
Modeling Term Structure and Related Concepts  407 
Classical and HJM Approaches to Fixed Income  426 
Classical PDE Analysis for Interest Rate Derivatives  451 
Integration in Stochastic Environments  204 
Itos Lemma  230 
The Dynamics of Derivative Prices  252 
Pricing Derivative Products  275 
Relating Conditional Expectations to PDEs  467 
Stopping Times and AmericanType Securities  489 
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Other editions  View all
An Introduction to the Mathematics of Financial Derivatives Ali Hirsa,Salih N. Neftci Limited preview  2013 
An Introduction to the Mathematics of Financial Derivatives Salih N. Neftci No preview available  1996 
Common terms and phrases
approximation arbitrage arbitragefree arbitragefree price asset prices assume assumption binomial Black–Scholes bond prices boundary condition calculate call option chapter coefﬁcients conditional expectation consider constant continuoustime convergence corresponding deﬁned deﬁnition denoted depend derivative asset deterministic diffusion discount bond discussed drift dynamics equal example ﬁnancial markets ﬁnd ﬁnite ﬁrst ﬁxed formula forward rates function Girsanov theorem given Hence increments inﬁnite inﬁnitesimal information set interest rate interest rate derivatives interval Ito integral Ito’s Lemma jumps Markov martingale maturity normally distributed notation obtain parameters payoff portfolio probability measure process Wt random variable represents respect righthand side risk riskfree rate riskneutral measure satisﬁed solution spot rate spotrate stochastic calculus stochastic differential equation stochastic processes Suppose Taylor series term trajectories underlying asset unpredictable variance volatility Wiener process zero