# Tagged Questions

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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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### Software for decomposing structured products into plain vanilla products

Nowadays structured products (or packages) with complex payoff diagrams are omnipresent. Do you know of any software, add-ons, apps, code whatever, that enables you to enter a payoff diagram or a ...
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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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### 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 ...
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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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### How to replicate this option?

I have a question I am not sure how to approach: Suppose interest rates is 50%, a stock worth \$1 today can be worth \$2, \$1, \$0.5 next year. If the option that pays \$1 only when S = \$2 is ...
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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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### 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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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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### replicating strategy three step binomial

I am having some trouble setting up a replicating strategy for a call option with a three step binomial model (discrete). I have no trouble doing this in a two step binomial model by backward ...
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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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### Determine state price vectors?

I have 3 states with two assets, stocks and bonds. The bond has a payoff of 1 in every state of the world. And the stock has a current price of $S_0 = 100$ and ...
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### Good book about replicating portfolios

I want to know if anybody can suggest me a good textbook which explains in detail and in an understandable way how to create replicating portfolios of financial instruments like options "cash or ...
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### Replication of the portfolio in single step binomial model

I would be grateful if anyone would comment how to construct this: Assume $S_{i}^k$ is a stock price at time level $i$ and at price level $k$. Assume option is written on $S$ with a a payoff \$f_{T}^{...
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### Reading Recommendations on ETF's / “Factor certificates”

I'm looking for some good papers on exchange traded funds, especially on so called factor certificates (e.g. 2x underlying long, so when the underlying moves 1% the certificate moves by 2%). My ...
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### Quantifing quality of cointegration

I'm trying to replicate instrument which is untradable. My approach is analysis of cointegration between it and three another time series (four variables in model) which correlates with it. I found ...