Questions tagged [replication]
The actual or hypothetical combining of financial instruments in a certain manner so that they have the same specified characteristics with a given financial instrument or portfolio.
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Replicating portfolio - must the underlying asset be used?
I am reading through famous sources like Hull, Wilmott, et.c., where they construct the replicating portfolio in a one-step binomial model. This involves setting up a system of equations, where we ...
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What is the purpose of risk neutral valuation vs replicating portfolio approach
I'm currently writing a bachelor's thesis on GPU accelerated option pricing algorithms. As a CS major I'm not knowledgeable on the higher level math, but I have tried learning the basics of option ...
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Confusion with replicated portfolio in Black Scholes model
I apologise if my question has been answered already however I could not find a complete explanation online.
My understanding of the derivation of the Black Scholes model is that given a derivative, ...
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Replicating call option by cash and stock under BS model
Suppose we are in a market following the Black-Scholes (BS) model, and we want to use cash and stock to replicate a call option.
We perform Taylor expansion of the call price $ V $ with respect to the ...
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BSM replication with expiry delta
I’ve been thinking about this problem and I’m missing something.
Assuming a BSM world, I sell an OTM option at strike K. I then proceed to delta hedge it at the strike K each time K is touched. Why ...
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Help me understand super replicating portfolio
Lets consider a hypothetical stock with current price of $S_t$ at time t and it can take any positive value with a strictly positive probability.
There exists a derivative that pays $ e^{S_T}$ at ...
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Understanding American option payoff at T+0
The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread.
I am trying to understand American options and to know if it has any significant ...
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Delta hedge for derivative in Black-Scholes market
Consider a derivative in the Black-Scholes market with the price formula $\Pi_t = F(t,S_t)$. I want to find a self-financing portfolio consisting of the stock and the bank account that hedges the ...
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How to replicate a claim in a stochastic volatility model?
Given a Markovian stochastic volatility model with an asset $S$ and a variance process $V$ given by
$$
dS_t = \mu_t S_tdt + \sqrt{V_t}S_tdW_t, \\
dV_t = \alpha(S_t,V_t,t)dt + \eta \beta(S_t,V_t,t)\...
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In the CRR model, describe the strategy replicating the payoff $X=(S_T-K)^{ +} +a(K-S_{T-2})^{+ }$ for $a \neq 0$ [closed]
In the CRR model, describe the strategy replicating the payoff
$X=(S_T-K)^{ +} +a(K-S_{T-2})^{+ }$ for $a \neq 0$
$X$ consists of two parts:
European call option with strike price $K$ and expiration ...
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Using Daily or Annual Volatility to Price an Option
From Joshi's Quant Interview book:
The statistics department from our bank tells you that the stock price has followed a mean reversion process for the past 10 years, with annual volatility of 10% and ...
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Questions about the replicating portfolio in the binomial model
I'm starting to teach myself quantitative finance and I've got several questions (marked in bold) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, ...
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Can I replicate an option with time to expiry $t$ by trading in another with expiry $T > t$?
Suppose there's a salesman who will always sell me an option expiring in two weeks. His options trade at a steep discount, but I can't directly arb it because the closest exchange-traded contract ...
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Pricing squared derivative: Equating S^2 + a strip of otm calls + a strip of otm puts = only calls
In Peter Carr, Dilip Madan, Towards a Theory of Volatility Trading, 1998, (also derived here by Gordon), both calls and puts are used to replicate any twice differentiable payoff. I suppose one would ...
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Modelling Bank deposit with replicating portfolio
I am trying to understand how deposits in bank are modelled, and one such modelling approach is replicating portfolio approach as provided in http://www.diva-portal.org/smash/get/diva2:1208749/...
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How do you price an option on fresh corn?
I'm preparing for quant interviews, and I had this question for myself. I'm not actually trading corn options. My goal here is just to better understand how to deal with these kinds of options.
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How to use PCA to find best portfolio replication
I have an exposure to 3 products. I have another 12 tradable products that I can use for hedging myself. I have the correlation matrix between the 15 (12+3) products.
How can I use PCA to find the ...
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Replicate a claim in a complete market
Consider the Black-Scholes market wher $\sigma > 0$, and a claim paying $S_T^{\gamma}$ at time $T$, where $\gamma$ is some positive constant. How do I find the replicating portfolio of such a claim？...
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Replication (binomial tree)
Hey what is the replication strategy on the binomial tree when I have for example 10 step model and dividend is paid at step 3? I have a well-written price tree but I do not know what the replication ...
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Replicating portfolio
I have a doubt about the replicating portfolio methodology.
Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
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Replicating a derivative
Assume an underlying random variable $S_T$ which satisfies that $S_T > 0$ and that $\mathbb{P}\{S_T \neq 100 \} > 0$.
Let $X_0$ be the time-0 price of a contract that pays $X_T: -2\log\left(\...
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Best approximation of a function as sums of calls
I have a function noted $u$ which I know the value on N points $s_{1} ,s_{2},.....,s_{N}$ we denote $u_{1},u_{2},...,u_{n}$ the values of u in these points and a grid of strikes $ (K_{i})_{1 \le i \le ...
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Index Replication
I am a first year university student.
I am trying to replicate an Index, for instance SP500. But instead of doing a full replication (by buying all the stocks), I wonder : How can I choose a portfolio ...
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Why do replicating strategies delta hedge?
We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral ...
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Finding a PDE for an option $V(t,r(t),S(t))$
I have 2 approaches in my mind for finding a pde of an option that depends both on the short rate as well as the stock price- $V(t,r(t),S(t)$. Are these equivalent?
Find a hedging portfolio by ...
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