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Martingale Property

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Expectation Operator

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OR Rule of Probability

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SABR

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Lookback Call Option

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Event Time

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Arithmetic Symmetric Random Walk

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Binomial Random Variable

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Markov Process

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Bellman Equation

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Supermartingale

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Optimal Exercise Policy

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Simple Binomial Stock Price Model

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Conditional Expectation Operator

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Deriving EoD PnL for Strategy of Buying & Selling Forwards in a Floating Rate World

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Deriving EoD PnL for Strategy of Buying & Selling Forwards in a Constant Rate World

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Event Sequence

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Equity European Put Option

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Portfolio Optimisation

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Dynamic Portfolio Hedging

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American Call Option

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Law of Total Probability

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Conditional Jensen's Inequality

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Jensen's Inequality

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Proving Jensen's Inequality of Conditional Expectation

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Demonstrating Convex Function Output is Submartingale for Martingale Input

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Geometric Symmetric Random Walk

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Showing Arithmetic Symmetric Random Walk is a Martingale

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Showing Transformed Geometric Symmetric Random Walk is a Martingale

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Submartingale

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Proving Shorthand Identity for a Stochastic Process

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Proving Stochastic Process is Markov

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Showing Discrete Time Stochastic Integral is Martingale

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Finding a Stochastic Process that is Martingale but not Markov

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Proving Martingales with Same Terminal Value are the Same at Any Time

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Proving Risk-Neutral Derivative Price Process is a Martingale

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Proving Risk-Neutral Expectation-Based Derivative Price Process is a Martingale

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Proving Two Different Pricing Methods Give Same Derivative Price

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Proving Risk-Neutral Price of a Call Option is 1.2

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Proving No-Arbitrage & Expectation Based Methods Give Same Option Price

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Binomial Option Pricing by Expectation

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Binomial Stochastic Volatility Model

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Risk Neutral Probabilities in a Binomial Option Pricing Model

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Option Prices for a Given Payoff

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Transient Underlying Delta Weights

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Targeted Conditional Delta Weight

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Option Pricing by Expectation

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Showing that Price of Option on a Dividend Paying Stock is Martingale

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Showing Option Pricing by Expectation Holds for Dividend Paying Underlying

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Showing Discounted Dividend Paying Stock Price is Not Martingale

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Portfolio Replicating a Lookback Option

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Constructing a Hedged Call Option Portfolio that Returns 25%

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Proving Jensen's Inequality

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Linearity of Expectation

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Asian Call Option

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T0 Value of Asian Call Option

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Filtration

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Proving Jensen's Equality

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Jensen's Equality

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Change of Measure

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Probability Space

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Showing a Two-Dimensional Process is Markov

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Radon-Nikodym Derivative

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Showing the Inverse of Radon-Nikodym Derivative is Always Strictly Positive

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Risk Neutral Pricing with Change of Measure

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Portfolio Process

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Wealth Process with a Simple Utility Function

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Optimisation by Lagrange Multipliers

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Objective Function

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Optimal Path to Maximise Binary Utility

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Algebraic Manipulation Approach

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Forward

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Optimal American Exercise Strategy

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Pricing by Discrete Expectation

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European Straddle

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Longstaff-Schwartz Model

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Potential Cashflow

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Fixed Cashflow

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Induction and Subadditivity Solution

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Lower Bound for American Put

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American Call Upper Boundary

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Exercise Time

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Deterministic Vol Asset Price Model

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Power Series

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Using Constrained Binomial Distribution

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Taylor Compression

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Hitting Time

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Taylor Compression Approach

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Risk Neutrality

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Random Walk Drift Identity

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Probability Condition

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Integrability Condition

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Standard Expectation Approach

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Reflection Principle

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Redundancy Elimination Trick

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Arithmetic Asymmetric Random Walk

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Simplification by Reflection Principle

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Stochastic Differential Equation

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\(\mathcal{P}_{PnL}\)

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PAP Hedging Portfolio PnL

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PAP Hedging Portfolio Underlying Units

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Verifying the Hedging Equation

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American Supermartingale

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Join Distribution of Current Level and Maximum-to-Date of Asymmetric Random Walk

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Join Distribution of Current Level and Maximum-to-Date of Symmetric Random Walk

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Expressing Optimal Terminal Portfolio Path in Terms of Order Threshold

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Optimal Exercise of American Straddle

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Optimal Exercise of an American Call

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Optimal Exercise of an American Put

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Optimal Asian American

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Probability of Hitting Boundary One

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Expected Discount

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Expected Finite Stopping Time

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Probability of Reaching Level Two

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Computing Finite American Put Values

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