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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FVA demonstration? [duplicate]

In the well-known article by Mr. Piterbarg "Funding Beyond Discounting". he demonstrates that the price of a derivative product in a multi-curve universe: Who also expresses it but without ...
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How do you explain consistently making money with discrete hedging a call option?

In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL ...
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Practically, are the prices of 0-strike European calls and stock identical?

By no-arbitrage, the price of a vanilla European call with $K=0$ should be that of the underlying stock (as selling the call is perfectly hedged by buying the stock). However, is this true in practice?...
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Gamma smoothing of vanilla options

I want to ask a question about the answer provided here: https://quant.stackexchange.com/a/35211/61083. I'm wondering if there is mathematical proof as to why it is working. Meaning if I reprice a ...
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Cash balance sign in hedging portfolio

Consider a derivative which depends on $n$ assets with price vector $X=(S^1,\dots,S^n)$. The derivative value $V_t$ is given by the function $v(t,S)$, so that the hedge ratios for the hedging ...
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black Scholes model hedging without constant volatility

I have started to look deeply in the hedging and I have created some simulations to simulate delta hedging strategies. I use BS model to calculate delta. The only issue was, which Volatility should I ...
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What are some interesting recent machine learning related developments in the QF domain?

In 2020 I wrote a MSc thesis on the hedging of exotic options using recurrent neural networks (loosely based on the paper Deep Hedging (2018)by Buehler et al.). Since then I have been interested in ...
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Do products exist to hedge against specific building materials?

I was wondering whether there exist product to hedge against specific building materials? Up to now I have not yet found a suitable product to hedge against cement or glass? If not, how would one ...
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Utility indifference vs Quadratic hedging for incomplete markets

What is the difference, if any, between the quadratic hedging and utility indifference approach to pricing/hedging in incomplete markets?
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Gamma squeeze - mathematical explanation

I am trying to understand from a mathematical and financial point of view the mechanism behind the so-called gamma squeeze. Is there a good source to read about this/ My questions are: what are the ...
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Optimal Hedging Ratio using Copula Models

Let $r_{s, t}$ and $r_{f, t}$ be the return rates of the spot and futures of a commodity at time $t$. The hedging ratio based on variance minimization is calculated by finding the minimum of the ...
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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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Pricing & hedging vanilla interest rate options with SABR LMM

Are there any advantages of pricing and hedging plain vanilla interest rate options with more complex SABR LMM instead of simpler SABR model? Should one always go with the SABR LMM as a universal ...
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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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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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Negative-gamma delta hedging (for a call option writer): how will the stock price affect the portfolio profit?

Suppose a (European) call option writer is hedging their risk by taking a long position in stocks (holding $\delta_C$ shares). The value of the portfolio is $V(S)=\delta_CS-C$. Then is the gamma of ...
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Hedging an option with a stock and forward variance

Following Deep Hedging under Rough Volatility (https://arxiv.org/abs/2102.01962) they construct a hedging portfolio consisting of a stock and a so-called forward variance to hedge a European call ...
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Leveraged Porfolio Hedging

What is the right approach to hedge debt of 1 dollar who's value changes based on a basket composed of: 32 cents of short Asset A 26 cents long Asset B 43 cents long usd The debt is leveraged by 2....
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How can I hedge basis risk?

Let's say we caught arbitrage between spot and futures, we sold futures and bought spot. The risk-free rate is 5%, and our arbitrage position profit is 5.5%. When the interest rates increase to 6% ...
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Fixed vs float swap interest rate risk

I have some technical questions about what are the best settings in Bloomberg to calculate the interest rate risk of a swap. When Bloomberg calculates the DV01, it simply bumps the par swap curve by +/...
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How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
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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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Delta Hedging with a Different Underlying

In Bouzoubaa and Osseiran page 68 equation 5.3, the authors discuss delta hedging a call written for asset $S_1$ using a different but correlated underlying asset $S_2$. The authors provide the ...
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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 to price OTC swaps to hedge non-economic cashflow variability

Suppose we have a stochastic cashflow $X_t$ from a portfolio of contracts with clients. We can simulate from $X_t$ and can calculate $E[X_t], \forall t \in [1,n]$ where $n$ represents the longest ...
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Gamma PnL when hedging with implied volatility - where is the mark to market PnL?

It is well known that hedging with implied volatility involves a PnL: $0.5*(σ^{2}_r−σ^{2}_i)S^{2}*Γ_{i}dt$ In the Wilmott paper (http://web.math.ku.dk/~rolf/Wilmott_WhichFreeLunch.pdf), they imply ...
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hedge ratio, calculating exposure and perfect hedge

Hi I know how to get the hedge ratio it is 0.9 but what is the companies exposure is it just 1 million? Once I know exposure I can calculate the rest of part (a). For part (b) I can someone explain ...
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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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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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Is it wiser to hedge downside risk with put options on an ETF, or Leveraged ETF, of the same index?

My pre-suppositions I must hedge against a POSSIBLE market crash. But I can't predict if and when. I hold no beliefs on volatility. Small caps crash faster than large caps. My question I plan to ...
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Why "hedging motives" and "heterogeneous preferences" are explanation for "under diversification puzzle"?

Han et al. 2021 documented something relating to the "under diversification puzzle": Standard explanations for under diversification include hedging motives and heterogeneous preferences, ...
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Delta hedging error in B-S (hedging with implied vol) question

I have been thinking about this for a while and am at my wits end. Now assume I am pricing a call at implied vol $s$, whereas the realized volatility is $σ$. Let $C$ be the incorrect pricing function. ...
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Currency hedging 3 month sterling libor futures

Each libor contract is 500,000 gbp. Can I hedge it by going short 8 gbp/usd futures per libor to hedge out currency risk considering each gbp/usd futures is 62,500 British pounds?
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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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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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Why are implied parameters preferred over expectations of future implied parameters?

For example, when we price options on assets under the Heston model, we often compute the volatility of the volatility of the price of those assets implied by the market at time $t=0$ using the market ...
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Trade anything?

I have a question after reading the post below. https://www.onlinebetting.org.uk/betting-guides/can-you-bet-on-anything-you-want.html Question: I want to bet on a niche topic or asset or anything that ...
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General question regarding delta heding

I was wondering if I have to take the strike prices of options into consideration when doing a gamma and delta hedging. As an example, let's suppose that I have 2 positions: a long position call ...
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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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Barrier shift consideration in delta hedging down and in puts (PDI)?

I have a question regarding the barrier shift used when risk managing a down and in put (PDI). I'm reading Exotic Options Trading by Frans de Weert and he gave this example. Trader is long one PDI 100/...
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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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What are the most common ways that quantitative funds construct industry/style-neutral factor portfolios?

For instance, consider momentum strategies. Naive portfolio construction will likely load on large style/industry return components, which increases portfolio risk dramatically. How do quant funds ...
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What is the point of hedging in this scenario?

I'm new to this stuff, and have the following question: In John C. Hulls book the following scenario is presented: on May 15 we enter into a contract to sell 1 mill barrels of oil for the market price ...
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Mark Joshi's book - quant interview questions

I am currently doing the question on pricing the option with payoff: $$\max (S(S-K),0).$$ On the relevant question section, it's asked why would a bank be reluctant to sell such option? I can't really ...
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Implementing a hedging strategy for oil future options

I am currently writing a paper examining two models for pricing options on WTI Crude oil futures, and I want to backtest hedging strategies from both model and compare them against each other. However,...
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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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A decent model to calculate hedges

Is there an option pricing model that wouldn't be too time consuming to set up in Python (for example) and that would provide better delta hedges than Black-Scholes? This would be mainly for equity ...
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FX Hedging costs when using 3m FX Fowards vs XCCY swaps for an IG Bond

Suppose I want to hedge the FX exposure of an USD Corp Bond(held to maturity) to GBP and I can choose between rolling 3m FX Forwards and XCCY swaps. How can I estimate the difference in the hedging ...
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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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Delta hedge error black-scholes by Mark Davis

I'm currently reading a paper by Mark Davis in which he talks about a delta hedging error in the Black-Scholes formula. The delta hedging error is given expressed as $Z_t$ with the formula: $$Z_t = \...

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