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Questions tagged [replication]

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0
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2answers
34 views

Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff ...
1
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0answers
60 views

Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...
2
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1answer
63 views

Profit and Loss on delta-hedged portfolio

The overnight profit formula from a textbook (possibly Derivative Markets by McDonald) is the following: $$\Delta _{t}(S_{t+h}-S_{t})-(V_{t+h}-V_{t})-(e^{rh}-1)(\Delta_{t}S_{t}-V_{t}),$$ where Delta ...
4
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2answers
171 views

Replicating the square of an option $C^2 (S,K,t,T)$

Given a vanilla options market, i.e. $C(S,K,t, T)$ for all strikes $K$, is it possible to replicate $C^2 (S,K,t,T)$? So I am looking for a self-financing portfolio which has a price equal to $C^2(S,K,...
3
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0answers
47 views

How to Compute the payoff of Var Swaps, which I have replicated

I used Derman(1999) method, to calculate the fixed Kvar for Variance Swaps using actual option price data. The first Pic Shows the outcome. (ignore the 0s). Now the profit and loss of short var swaps ...
1
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2answers
90 views

ETF Replication

I have a question regarding the ETF replication methods. I know there are two main methods, namely physical and synthetic replications, but I would like to understand how an ETF trader can : ...
1
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1answer
66 views

Cash deposit in replicating portfolio for BS equation unnecessary?

The book on Option Valuation Methods that I currently study (Higham 2013) constructs a replicating portfolio $\Pi = A(S,t)S + D(S,t)$ for deriving the BS PDE, where $D$ is a cash deposit. $D$ does not ...
1
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1answer
52 views

Static hedge forward swap using zero coupon swaps

I'm trying to create a static hedge for a forward swap using two spot starting zero coupon swaps (to prove that there is no convexity adjustment needed). Here are the instruments - Paying fixed in ...
1
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1answer
114 views

Replicating an option

When we replicate a portfolio of cash and stock for a call option, shouldn't the replicating portfolio's greeks be equal to options greeks? Is that true? If it is, how is it that a portfolio of cash ...
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0answers
50 views

Replication error of a long dated product

My question is a bit general : Hedging/Replicating a long-dated (FX) product with short-dated (FX) products leads to a replication/hedging error most of the times. Is it possible to quantify this ...
2
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1answer
611 views

CMS options, cash-settled/physically-settled swaptions

CMS options are traditionaly replicated using a theoritical "continuous" strip of swaptions (see for instance Hagan's paper "Convexity Conundrums : Pricing CMS Swaps, Caps and Floors"): In the paper,...
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0answers
73 views

Price futures option via replication

I ran into some difficulties when trying to price a futures option via replication in a simple one-period binomial model. I am quite aware that this is easy with risk-neutral probabilities and ...
1
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1answer
62 views

Pricing weighted/average stock price claim

In a market consisting of a bank account with a constant interest rate r and a non-dividend paying stock S, consider a T-claim that pays $X = S(T)/S(T_0)$ at time T, where $T_0 < T$. a) ...
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1answer
496 views

Replicate a Portfolio with Given Payoff

Looking for a convincing general strategy [not trial and error] to solve these kind of questions: Any help will be super helpful! Thanks a bunch! Replicate a portfolio on an underlying asset $S$ ...
2
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1answer
199 views

Binary option analytical formula

Given $r=0$, $\sigma(K)=\text{const}$ and: $$ \text{Binary} = \lim_{ε → 0} \frac{(C(K,\sigma (K))-C(K+ε,\sigma(K+ε)))}{ε} $$ I have to find the analytical expression for the above. Since $σ(K)=\...
3
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2answers
237 views

What Positions on an Underlier CANNOT be Hedged with Vanillas?

Say I have infinite precision of strikes $K$ (continuous world $dk$) and expirations $T$ (continuous $dT$) all with liquidity (so no practical limitations). What positions in an underlying can't be ...
3
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0answers
34 views

Infinite Horizon Barrier Option Paradoxe [duplicate]

I've came across this question which is puzzling me. Imagine that interest rates are zero and that you observe a stock $S_t$ whose value today $S_0$ is equal to 1\$. We consider the derivative that ...
3
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1answer
138 views

Replicating a square derivative with calls and puts

I have a derivative that pays off $S_T^2$ at time $T > 0$ with $S_T$ denoting the price of a non dividend-paying stock at $T$. I came across a question about how one can statically replicate this ...
2
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1answer
191 views

Collateral replication argument

I'm trying to follow the replication argument in the first page of the following paper http://www.math.columbia.edu/~fts/Collateralized%20trade%20pricing%20made%20simple%20v1a.pdf One can however ...
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0answers
182 views

Is the replication porfolio for a European Call, self financing for changes in time?

I was reading slide 29 here: http://people.hss.caltech.edu/~jlr/courses/BEM103/Readings/JWCh11.pdf (mirror) Sub-heading: "An interpretation of the Black-Scholes formula" It is saying that the below ...
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1answer
280 views

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 ...
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0answers
197 views

The difference between hedging and replicationg methods of deriving option prices

For deriving, say European, option prices, is there a difference between the replication approach and the hedging approach? More specifically, is there a situation where the hedging approach will not ...
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1answer
181 views

Super Hedging in incomplete Trinomial Tree

I have a question concerning the super-replication of a call in a trinomial tree which has the following characteristics: Suppose we have one risky asset $S_t=2+\sum_{k=1}^tZ_i$, where $P(Z_i=0)=P(...
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0answers
80 views

Writing option on one's own default

Maybe this is a weird question, but suppose that, for some reason, one would like to write an (implicit) option whose payoff is indexed on the writer's CDS spread. I would like to know what would be a ...
7
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1answer
1k views

delta-hedging is failing

and thank you for answering me ! While I was recently testing a delta-hedging on a few products, I got a P&L result of 20% for some of them. First, I thought that the implementation was ...
2
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1answer
80 views

How bad off are we when we use the “regular delta replication” strategy in an FX market on a Quanto?

See this question for context: https://quant.stackexchange.com/questions/32725/dynamic-hedge-of-quanto-options#= In there, I expressed interest in how well the usual strategy of replicating an ...
1
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1answer
123 views

Why does this delta hedge work, and what to do in more general circumstances?

In the simple Black-Scholes model, we can replicate an option by investing its $\Delta$ in the underlying, and keeping that portfolio self-financing via the bank account. I have two questions. I don'...
2
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0answers
413 views

interview question : replication strategy of a betting game

Here is a question I found in a book I am not able to finish. Your help will be much appreciated! I also included where I have been so far. Q: Team A plays team B in a series of 7 games, whoever wins ...
2
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1answer
161 views

Calculating the annual return on an option using a replicating porfolio

I am self-studying and encountered the following problem: My idea was to calculate the price of the put using a replicating portfolio, then use the formula: $$Pe^{\gamma h} = S\Delta e^{\alpha h} + \...
0
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1answer
41 views

Signs for the assets in a portfolio and definition of portfolio value

Suppose that we have a market with a stock, modelled by $\{S_t\}_{t>0}$ and a riskless money market account $\{B_t\}_{t>0}$. Consider a strategy $\{ H_t^B,H_t^S\}_{t>0}$ be a portfolio over ...
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1answer
222 views

Finding the replicating portfolio a European T-claim (put)

I have $$dX_0(t) = ρX_0(t)dt ; \qquad X_0(0) = 1\\ dX_1(t) = αX_1(t)dt + βX_1(t)dB(t) ; \qquad X_1(0) = x_1 > 0$$ as the classical Black-Scholes market. I a trying to look for the replicating ...
3
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1answer
669 views

Understanding the relationship between the Black-Scholes formula and a replicating portfolio

I'm self-studying and I'm considering the below example. The specific example is not especially relevant, but I included it for reference. I'm trying to understand the relationship between a ...
1
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1answer
163 views

Quanto Total Return of a Foreign Asset into Domestic

Say we have a product that pays the following at expiry $T$: $$\text{Payoff}_{in\ USD} = \text{Notional}_{in\ USD} \cdot \frac{DAXLevel_{in\ EUR}\ at\ t=T}{DAXLevel_{in\ EUR}\ at\ t=0}$$ i.e. it ...
4
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2answers
204 views

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 ...
2
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0answers
46 views

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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0answers
76 views

Replicating portfolio: initial portfolio?

I have a bit of trouble understanding how to determine the replicating portfolio of a call using just a stock and the riskfree asset. I have times $t = 0,1,2$, and at time $2$, we have $3$ payoffs ($...
2
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1answer
198 views

Which studies should be replicated?

In psychology voting on which studies should be replicated is established on a website. For economics, including financial economics, the ReplicationWiki (that I founded) offers a voting option but it ...
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0answers
90 views

Hedging American Derivative

Reading the book by Andrea Pascucci "PDE and Martingale Methods in Option Pricing", pp. 84, I found something that appears inconsistent to me. It concerns the construction of the optimal portfolio for ...
2
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0answers
146 views

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 ...
0
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1answer
105 views

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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1answer
75 views

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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2answers
125 views

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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1answer
424 views

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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3answers
2k views

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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3answers
468 views

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 ...
3
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1answer
169 views

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〗 ...
3
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2answers
1k views

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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0answers
522 views

Simple Forward Interest Rate Proof

Just trying to check my logic here: Let $Z(t,T)$ be a Zero-Coupon Bond with maturity $T$ bought at time $t$, $S_m$ be the spot interest rate for time $m$ and $S_n$ for time $n$ respectively, where $n ...
2
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1answer
3k views

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 ...
0
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1answer
126 views

Under an EMM, does there necessarily exist a replicating portfolio?

In general, under an EMM, does there necessarily exist a replicating portfolio for every derivative? I believe the answer to this is false. A simple example is a discrete time, trinomial model. ...