Questions tagged [hedging]

[Think of it as insurance. When people decide to hedge, they are insuring themselves against a negative event. This doesn't prevent a negative event from happening, but if it does happen and you're properly hedged, the impact of the event is reduced. So, hedging occurs almost everywhere, and we see it everyday.](http://www.investopedia.com/articles/basics/03/080103.asp)

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Bridgewater's Daily Observations

Bridgewater Associates send out Daily Observations to their clients, but I haven't found many traces of these publications online. The series started some 40 years ago by Ray Dalio, and there're just ...
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American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t. $$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
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Non attainable claim - Incomplete market

I am wondering whether there is a standard procedure to find a non attainable (i.e. non replicable) asset in an incomplete market. As an example, let us have the following market ($B = (B^1, B^2, B^3)$...
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Intuition behind the Carr and Wu (2014) static hedging for ordinary options

Let $(S_t)_{t \geq 0}$ be the price of an underlying asset, $r$ be the risk-free rate of return, $q$ the dividend yield, $C_t(K,T)$ is the price of a call option written on $S_t$ at time $t$ with ...
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Formal proof market incompleteness under jump diffusion

Does anyone have formal proof of markets incompleteness under jump diffusion ? I am familiar with the intuitive approach as mentioned in Tankov (delta), yet I am looking for a formal approach and ...
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The concept of an incomplete market

While skeeming the relevant literature and web-sites I noticed that mostly the concept of the incomplete market is reduced to the following statement "A market is incomplete if there are more ...
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Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
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Pricing and hedging of vanilla options based on non-tradable underlying

Consider a non-tradable stock index $S$ which satisfies: $dS_t=\mu S_tdt+\sigma S_tdW_t$ and a risk-free asset $B$. I want to price an European Call option with the payoff $C_T=max(S_T-K,0)$. The ...
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Delta hedging the day before expiry

In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? ...
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How often to tune the regularisation parameter in LASSO?

I'm trying to implement the following paper: Avellaneda & Lee (2010), Statistical Arbitrage in the US equities market. To build the strategy, the idea is to trade a stock and hedge using a basket ...
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What put options would the Universa Tail Fund have bought?

According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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Should you hedge theta?

Consider an arbitraty interest rate derivative $C$. Assume that in order to hedge it, you are allowed to construct portfolio $H$ of linear combination of simple instruments such as Interest Rate Swaps ...
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Classic dynamic delta-gamma hedging in Python

I am trying to run a delta-gamma hedge for a Black-Scholes model in Python.The Euler disceretizatioin of the paths is the simplest possible. I wrote the code below but the PnL looks undesirable and ...
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Uniqueness of the Hedging strategy

I am currently reading the book "Nonlinear Option Pricing" by Julien Guyon. In the book they defined an attainable payoff $F_T$ as a $\mathcal{F}_T$ measurable random variable for which there exists ...
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Hedging cross gamma

I understand how to hedge delta and gamma risk. Could someone explain to me how cross gamma hedging is done by the trading desk. In particular I am interested in hedging for interest rate exotics. So ...
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Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
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Motivation for hedging volatility using VIX ETNs

I wondered what the motivation for professional investors could be to trade in VIX ETNs. Why would they even think about trading this kind of product? (They normally should have access to VIX options,...
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What is the correct hedging strategy using futures?

In practice, even without maturity and underlying mismatch, hedging using futures does not always require a one-to-one hedge ratio. Tailing factor needs to be considered. Suppose the current spot ...
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Calculating the Hedge Ratio

Suppose we have an index whose value is calculated by a weighted geometric mean. Now we want to recreate the index using its underlying components. How would we go about calculating the hedge ratios ...
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How do you hedge volatility risk?

Suppose I model an asset $S_1(t)$ under a stochastic volatility model. To price an option on $S_1$, I must assume the existence of an asset $S_2$ that is used to hedge against changes in the ...
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Net delta and gamma profile of a put spread

I have a question regarding the description in Simon Gleadall's book -- option gamma trading which you can find a copy HERE. The following paragraph he discussed about gamma and delta profile of a ...
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How to find percentage of FX exposure hedged through financial statements

I am analyzing a company's annual report, and wish to find the percentage of FX exposure they have already hedged. I have the following information: The net FX exposure for 4 different years The ...
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Empircal data analysis delta hedge error of Black-Scholes by Mark Davis

Regarding Mark Davis derivation of the delta-hedging error occuring in the black-scholes as a result of difference in realized volatility and implied volatily. The formula reads as follows: $$ Z_t = \...
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Are there any studies on the link between energy markets and hedging-strategies for Cryptocurrency mining?

Full Disclaimer: I first asked this question on Bitcoin.SE, however I feel like my question is more relevant to this site as there would be wider knowledge and insight of some better sources or ...
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Arbitrage portfolio example

Can you give me a concrete example of a self financing portfolio which gives arbitrage opportunity in the two-dimensional Black-Scholes model? By the two-dimensional Black-Scholes model I mean $$dS_{1}...
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2 votes
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Garch models - are they useful for hedging? If so how?

I understand that Garch models are useful to predict volatility. But are they useful for hedging in practice? If I want to hedge volatility, why shouldn't I just use a Variance Swap? In other words, ...
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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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Tailing the Hedge for Minimum Variance Hedge Ratio (Hull, 10ed)

I am an amateur reading Hull's Options, Futures and other Derivatives. I have encountered an issue similar to the one here: How to tail a hedge? (Question 3.26 from Hull, edition 10). The author ...
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Replicating portfolio with stock, bond and call option

I am trying to interpret: I am having trouble interpreting the replicating strategy: Context: $\phi$ is a generic payoff function, 0 < S < $\infty$, assumed throughout to be twice ...
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what is the state of the art method for hedging barrier options?

I want to create my own Barrier options for some security, I want to trade. I did some literature review, and found a static replication method, and many dynamic replication methods. I want to know ...
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Creating a hedge portfolio out of 10 assets

Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model? I have chosen 3 factors: excess market return, SMB and HML from ...
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2 votes
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Hedging jump models with a infinite number of derivatives

First of all, I inform you that I am not a financial mathematician and have vague knowledge about an incomplete market. Stochastic volatility models are incomplete so derivatives cannot be ...
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2 votes
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356 views

Discrete time option gamma hedging

1) An option $V$ under the Black-Scholes model is perfectly hedged when it is delta hedged continuously with the underlying $S$. When the hedging time is discrete, the delta $\Delta$ needs to take ...
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How to verify if beta "works" for hedging?

Suppose you want to calculate the beta of a stock to an index using weekly returns. If the stock is sufficiently volatile, and you use few enough observations, it is possible that the absolute value ...
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Using PCA to identify proxies for highly illiquid assets?

Was wondering if anyone had any literature to share on the use of PCA to identify proxies for highly illiquid assets? Say for example I have sold an option on stock A, an index constituent, and would ...
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2 votes
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Need some suggestion about short vxx long vx future strategy

I read a post by M. Avellaneda trading volatility At page 59-62 there's Strategies with VIX futures to hedge short VXX I'd like to reproduce the result. I am not sure how to do it. Some key points ...
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Delta hedging and PF-value

Imagine buying a call option and shorting the delta. After some time $dt$, the stock price changes, and so does the delta and the call option value. We re-adjust our hedge using this new delta. ...
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Relative Value Trading of American Style Options on Futures, Calcuating hedging ratios?

I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin ...
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2 votes
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References about market neutral portfolios that isolate unsystematic risk

I am looking for references, information, backtests etc. about market neutral portfolios that go long the index and short stocks of that index with high unsystematic (idiosyncratic) risk. The idea is ...
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Portfolio optimised for diversification and regular yield. How to hedge?

Here is a portfolio optimisation for equity dividend and yield designed to diversify holdings and produce regular monthly returns using only ETFs complete with R code. http://prescientmuse.blogspot....
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Market Exposure and Hedging

Normally the Market exposure associated with your stock/portfolio is your delta for that stock/ portfolio. Basic idea of hedging involved here is buying/selling respective futures depending upon ...
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Superhedging in Cox-Ross-Rubinstein model revisited

I am doing the following exercise from a math finance textbook but I got stuck at the end of the part 2. I found nothing on the internet concerning solutions of exercises from this textbook (called ...
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Constructing a Replicating Portfolio : Regression on Individual Constituents or their Average?

I would like to replicate a portfolio of stocks $S_1, \cdots, S_n$ using other instruments, $X_1, \cdots, X_m$. Using the letters above with a subscript $t$ to denote the forward returns over some ...
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1 vote
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Hedging large single asset positions

I recently came across an article that described how big market participants like GS, JPM, etc. take off large equity positions (block trades) of their clients, and putting that risk on their own ...
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Purpose of Vega Hedging

I am trying to understand the principle of vega hedging. When should a market maker vega hedge his position ? Let's suppose that a market maker delta and gamma hedge himself, and carries his position (...
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1 vote
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How does a hedged portfolio account for other greeks?

So a classic delta-hedged portfolio on a call option is: $$-C - \Phi(d) \cdot B + \frac{d}{dS}C \cdot S = 0$$ How is risk of other Greeks hedged? Is it something like this? $$-C - \Phi(d') \cdot B + \...
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Do option values depend on whether a trader hedges with a long stock or short stock position?

Sheldon Natenburg in his book Option Volatility and Pricing in the chapter on Risk Management is trying to explain the effect of interest rates on options. He says The value of a stock option will ...
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Hedging or Relative Value Strategies with Rho or Tau Correlations?

I understand that the Pearson correlation indicates the strength of linear relationship between two data sets. The applicability of this to hedging strategies is intuitive: If I can establish a linear ...
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1 vote
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Hedge robustness of the one factor Hull White model

I recently came across a quote in a book: "All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
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1 vote
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Interest rate hedging using treasury futures – timing and duration

I'm pondering over the following (rather standard) problem: We have \$10 million invested in government bonds and are concerned with highly volatile interest rate over the next six months. We want to ...
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