# Tagged Questions

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### How to replicate a correlation swap using only vanilla options and underlying

Assume I have two assets A and B that are positively correlated most of the time. I'm trading a strategy based on this correlation. Is there a way to protect myself in the event that the correlation ...
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### Reference Request: Trader Replication

I am looking for any reference where the following problem was addressed: given the list of trades of a trader teach an AI to replicate that trader's strategy. There are several well-known results ...
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### How to properly assess the costs of replicating an index via futures contracts?

I would like to validate this sentence, coming from a WSJ article: The cost of holding a Eurostoxx 50 future, for example, has climbed from an average of 0.07% of the contract value since 1998, ...
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### Proving there exists no arbitrage opportunities given 3 states and 2 assets

Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 ...
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### Variance swap replication and variance vega

Noob here. I've been trying to gain a better understanding of variance swaps and what better way than to replicate it with a portfolio of better understood instruments. I have read the GS 1999 ...
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### Replication of a call option by cash-or-nothing digital option

I am so stuck on this question: Consider a two-asset model where asset 0 is cash, so that the price of asset 0 is $B_t=1$ for all $t \geq0$. Asset 1 has prices given by $dS_t = a(S_t) dW_t$, where the ...
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### Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
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### Black-Scholes Equation - Riskless portfolio derivation

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
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### Cloning Return Streams

How would one go about cloning/replicating returns of a hedge fund or a strategy. That is given a return series of the object to be clone, is it possible to decompose return and reconstruct another ...
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### Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
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### Which objective function should I choose to minimize tracking error?

Let say I have $n$ assets and their returns over $m$ periods which are represented by a matrix $X \in \mathbb{R}^{m \times n}$, and I have some other asset with return over the same period which is ...
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### What is the instantaneous P&L of a Variance Swap?

What is the instantaneous P&L of a variance swap. Is it $(\sigma^{2}_{t}-\sigma^{2}_{implied})dt$?
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### How to run an asset replication regression?

I am doing extensive research on portfolio replication and was hoping to get some help with some problems I am encountering. I am running a regression between 2 assets that I believe replicate ...
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### What is a self-financing and replicating portfolio?

I try to understand the derivation of the Black-Scholes equation based on the "constructing a replicating portfolio". From mathematical point of view it looks simple. We assume that: Stock prices ...
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### What is the replicating portfolio of swaptions for a constant maturity swap (CMS)?

How do you replicate the payoff of a constant maturity swap rate? That is, if the payoff of a contract pays the 5-year swap rate every year for 10 years, how would you replicate this payoff using ...
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### Why hold options when you can dynamically replicate their payoff?

When holding vanilla options, you can cancel out, theoretically, all risk with dynamic (delta) hedging. Then you earn the "risk free rate of return". Why would you make such a portfolio when you can ...
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### Duality between constant rebalanced portfolio (CRP) and corresponding derivative

One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative ...
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### How to calculate equivalent futures position?

Let's say I have the following two positions: Buy ATM SPX call, expires in 1 month Sell ATM SPX put, expires in 1 month This creates a synthetic futures position. How do I calculate how many ...