# Linked Questions

13 questions linked to/from Black Scholes differential
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### Derivation of BS PDE problem using Delta hedging

I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ...
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### Merton model riskless self-financing derivation

Suppose $dA_t = A_t[\mu dt+\sigma dW_t]$ (assets' value) under the physical measure, plus the other assumptions of the Merton model. Suppose further that debt and equity are tradeable assets that ...
2answers
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### Expected value of delta-hedged portfolio

Consider portfolio in black-scholes world $\Pi = \Delta S - V$, where $S$ is the stock price and V is the price of the option. I have read that if we set $\Delta = \frac{\partial V}{\partial S}$ ...
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### What is a Short Option Hedging Portfolio?

In his book 'Stochastic Calculus for Finance II' Shreve uses the term: 'Short Option Hedging Portfolio' on page.156 (4.5.3). Can someone please explain this term with some kind of an example? It is ...
2answers
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### Dynamic Delta Hedging And a Self Financing Portfolio

Let's assume the usual Black Scholes assumptions hold. My question is related to an answer on this question. There, the weights ($\Delta_t^1$,$\Delta_t^2$) are derived which form a locally risk free ...
1answer
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### Replicating a portfolio with a certain payoff function

Assume there are two stocks $S_1$ with price $p_1(t)$ and $S_2$ with price $p_2(t)$ where $t$ indicates time. Assume, there is a hypothetical derivative $D$, which is such that, price of $D$ at a time ...
1answer
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### Notion of risk-less portfolio in derivation of Black-Scholes

EDIT: As pointed out by Gordon in the comments, the portfolio I considered in my original post is neither self-financing nor (locally) risk-free. Though the central question is still open. Suppose ...
1answer
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### Delta hedging and PF-value

Imagine buying a call option and shorting the delta. After some time $dt$, the stock price changes, and so does the delta and the call option value. We re-adjust our hedge using this new delta. ...
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### Is my derivation of Black-Scholes equation correct or am I missing something (eg assumption)?

Question: The following is my derivation of the Black-Scholes equation. Is it correct or am I missing some details (eg assumption)? Let $V$ be value of an option. Suppose value $\Pi$ of a portfolio ...