Samenvatting - Stochastic Processes: The Fundamentals
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Course
Stochastic Processes: The Fundamentals
Institution
Vrije Universiteit Amsterdam (VU)
Samenvatting Stochastic Processes: the Fundamentals van de Master Finance aan de VU (keuzevak voor Financial Econometrics). De samenvatting omvat de volgende onderwerpen: no-arbitrage pricing, risk neutral pricing, derivative pricing, binomial tree model, algebras and filtrations, markov processes,...
Learning Goals
• No-Arbitrage Principle: Students should understand and apply the concept of no-
arbitrage, which ensures there are no opportunities to make riskless profits in the
market.
• Continuous-Time Models: Gain familiarity with continuous-time financial models,
including concepts like Brownian Motion and stochastic processes.
• Itô’s Lemma: Learn to apply Itô’s Lemma, a fundamental result in stochastic calculus,
used in modeling financial derivatives.
• Black-Scholes Model: Develop a deep understanding of the Black-Scholes option
pricing formula, a cornerstone of modern financial theory.
• Risk-Neutral Pricing: Comprehend the risk-neutral pricing method, which finds
the fair value of derivatives by discounting the expected payoff under a risk-neutral
measure.
No-Arbitrage Pricing
Definition
The no-arbitrage pricing approach dictates that financial markets are structured in such a
way that there are no ”free lunch” opportunities, i.e., there are no riskless profit opportuni-
ties.
Arbitrage Opportunity
An arbitrage opportunity is a scenario where a portfolio has an initial value of zero, cannot
lose value, and has a positive probability of generating a profit.
Simple Example of Arbitrage
Suppose a coin toss pays EUR 10 for heads and EUR 20 for tails. If the cost to enter this
game is EUR 5, an arbitrage opportunity exists since the expected payoff (EUR 15) exceeds
the cost.
Generalizing to Markets
In financial markets with various traded instruments, arbitrage-free conditions mean that if
two assets or portfolios have identical future payoffs, they should be priced the same.
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