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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option replication
I understand the replication process for an option using black scholes formula. For example, for a call option replication, I can own delta units of shares and borrow money. The total portfolio is ...
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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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Synthetic replication of a spread option payoff
I have two assets, $S_1$ and $S_2$, and a European exchange-one-asset-for-another call option, such as those introduced by Margrabe (1978). So my payoff at expiration is the difference between the ...
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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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Hedging gamma, theta or other risks
Speaking on a high level, in the Black-Scholes model the $f\left(T,S_{T}\right)$ payoff's value dynamic is given by
$$df\left(t,S_{t}\right)=\left(\frac{\partial f}{\partial t}\left(t,S_{t}\right)+\...
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Understanding American option payoff at T+0
The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread.
I am trying to understand American options and to know if it has any significant ...
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Shout option payoff replication
I have not seen much talk about exotic options, and if they are actually traded. Is it possible to replicate the payoff of a ‘Shout option’ using standard European/American call and put options?
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Delta hedge for derivative in Black-Scholes market
Consider a derivative in the Black-Scholes market with the price formula $\Pi_t = F(t,S_t)$. I want to find a self-financing portfolio consisting of the stock and the bank account that hedges the ...
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Luck versus Skill in Mutual Fund Returns (Fama-French 2010)
I am reading carefully Luck versus Skill in Mutual Fund Returns (Fama-French 2010), and actually trying to replicate their findings. I have always found Fama-French papers well written, but they seem ...
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How to replicate a claim in a stochastic volatility model?
Given a Markovian stochastic volatility model with an asset $S$ and a variance process $V$ given by
$$
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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Is the self-financing condition necessary/"useful" in practice outside of replication/valuation?
I know that the need for a portfolio/strategy to be self-financing (the purchase of a new asset needs to be funded by selling of an older one/ones) is very helpful when attempting to price derivatives ...
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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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Static vs Dynamic Replication
These are extension questions to Joshi's Quant Interview Book.
(1) Given the choice between two different static replicating portfolios that match an option's payoff, what criteria would you use to ...
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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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Options skew: when is a perfect fit desirable?
I'm still troubled by a rather basic question, namely when is a perfect fit to the vanilla skew really necessary?
I think if you are trading vanilla options and/or Europeans that can in theory be ...
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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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Pricing and hedging caps and floors on illiquid emerging markets
I'm tasked with the problem of setting up a cap/floor trading on an emerging market which doesn't have any interest rate derivatives traded yet besides plain vanilla interest rate swaps. We intend to ...
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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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Does the put-call-parity hold for the Heston model? [closed]
My question is quite simple: Does the Put-Call-Parity hold for the Heston model? My textbook handels the Black-Scholes model with the Put-Call-Parity being
$$p_t = Ke^{-r(T-t)}+c_t-S_t.$$
However, it ...
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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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Is it possible to replicate the payoff of a portfolio of options taken from a set of strikes {K1}, given another set {K2} with the same underlying?
Let's say I have 2 different and independent (can't be mixed) set of strikes, {K1} and {K2}. If I create a portfolio of options using the first set and calculate my payoff at expiration, would it be ...
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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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Replicating a bond
In Shreve's Stochastic Calculus for Finance Volume II, section 6.5, page 273, Shreve talks about pricing a zero-coupon bond.
A zero-coupon bond is a contract promising to pay a certain "face&...
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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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Replicating Bloomberg Barclays index and sub-index monthly total and excess returns using constituent-level index-data
Bloomberg Barclays index returns (e.g. LF98TRUU Index "index_total_return_mtd" & "index_excess_return_mtd") and sub-index returns (e.g. BCBATRUU Index "...
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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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For what options does the "delta hedging rule" apply?
I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In chapter 4, he derives the "delta hedging rule":
$$\Delta(t) = c_x(t, S(t)) \text{ for all } t \in [0, T)\text{.}\tag{1}$$
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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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Strategy of replicating a portfolio with payoff $\int_0^T \frac{dS_t}{S_t}$
Given the asset price $S_t$ which is defined as follows
$$\frac{dS_t}{S_t}= r_tdt+\sigma_tdW_t$$
where $r_t$ is not necessarily deterministic.
What is the strategy of replication of the portfolio with ...
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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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Implementing a replicating strategy from the order book
So I have futures data in an order book (one screenshot every day at 12 p.m. for one month) for various futures products (i.e. various delivery periods such as the next day, the day after and so on) ...
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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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Replication of European swaption
Suppose we have a European payer swaption with 5-year maturity and 10-year tenor. The underlying is clearly the 10-year tenor payer swap. Does it mean that to replicate the swaption I need to ...
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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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Is there a general method by which we can replicate a given payoff? [duplicate]
I've been studying how to replicate different payoffs using options and zero-coupon bonds, and each time there's a different approach to solving the problem. I've been wondering if there's a general ...
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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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Hedging costs and BS-price
I'm looking at the chapter, "The Greek Letters" in Hull's book (Options and derivatives...) and in particular the paragraph "Dynamic Aspects of Delta Hedging". He demonstrates two ...
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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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Capped Variance Swap // Fair volatility using replication portfolio
I know that the Heston volatility model should be the best approach for computing fair volatility on capped variance swap but is there a way to estimate it from replication portfolio?
What I call ...
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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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How is the implied risk neutral density affected when changing numeraire?
For example i would like to price
\begin{equation*}
E^{Q} \left[ e^{-\int_{0}^{T}r_{s}^{cur}ds} f \left( S_{T_f}^{cur_1} \right) | \mathcal{F}_{0} \right] = B_{cur}(0,T)E^{Q^{cur}_{T}}[ f(S_{T_f}^{...
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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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Pricing multidimensional equity
How would you price \begin{equation*}
\mathbb{E}^{Q} \left[ e^{-\int_{0}^{T}r_{s}ds} f \left( S_{T_f}^1, S_{T_f}^2 \right) | \mathcal{F}_{0} \right]\end{equation*} with $T_{f} \le T$ and $S^{1}, S^{...
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How does a pricing model 'understand' the cost of hedging?
Suppose I am pricing a multi asset at the expiry payoff. Theoretically I define their joint distributions in the risk neutral measure, and price using expectation. However, how do I know that the ...
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Replicating portfolio of an option and to find inital price
I am very new to financial math so I am not sure how to do with this question. A friend sent me this question to practice but I am unsure how to begin. I read about call option . Can that be used for ...
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Constructing a replicating portfolio of a long-only strategy using long-short factors
Lets say I want to estimate a replicating portfolio by doing a linear regression between the returns of a long-only portfolio and several long-short factors like Fama-French 5-factor or Betting ...
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Black-Scholes market and payoff with integrals
I am struggling with the following exercise:
Prove that on Black-Scholes market, with some parameters $r, \mu, \sigma >0$,
a payoff
$$X=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\sigma}\...
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Black-Scholes Delta value at maturity?
Having to implement a replication strategy for European options, I encounter the following problem:
Delta tells me how many shares to hold at time t in my replication strategy. To do so, I simply ...
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Replicating a put option when short selling the underlying is not allowed
Suppose we sell a put option with maturity $T$, strike $K$ and fee $P_t=v(t, S_t, T, K, ...)$. The replicating portfolio consists of holding $\alpha_t = \frac{\partial{P}}{\partial{S}}=:\Delta_t$ ...
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Throwing a dice and risk neutral probability
Consider the game of throwing a "fair" dice. Not sure if the answer is obvious but is there any proof (e.g. replication argument) that under the risk neutral measure the probability of any outcome is ...