Questions tagged [hedging]

Financial strategy used to offset potential monetary losses or volatility.

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Unhedged factor models in trading

Suppose I have a factor model that takes in unemployment and GDP as $X_1, X_2$ respectively in estimating the fair price of asset $Y$. Say I observe that the market price of $Y$ has deviated ...
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Updated Methods for deriving the "front month equivalent" series in commodities derivatives

It is common in commodities markets to hold many positions, both long and short, across a range of contract months beginning in the prompt month to five or more years out. [My question is:] What is ...
2 votes
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Exact delta-hedging for endogenous payoffs

I would like to derive the exact delta-hedging strategy in the Black-Scholes market to replicate the following non-standard endogenous payoff. The particularity is that the payoff does not only depend ...
1 vote
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294 views

How do banks and dealers effectively hedge a variance swap?

It is known that a variance swap can be replicated by a strip of options. However, it is costly to trade that many OTM options and there is not enough liquidity to trade the wings in the quantity that ...
36 votes
5 answers
19k views

Skew arbitrage: How can you realize the skewness of the underlying?

It's not clear to me how to realize skewness. In other words, how do you implement skew arbitrage? There seems to be no well-known recipe like in volatility arbitrage. Volatility arbitrage (or vol ...
1 vote
1 answer
372 views

Portfolio optimization on a subset of assets

My objective is a portfolio optimization of the type: given $N$ assets with expected returns $r_i$ and a fixed portfolio size $M$, with $M < N$, find weights $w_i$ (positive or negative) maximizing ...
3 votes
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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 ...
7 votes
1 answer
1k views

Vega in the Heston model

I'm trying to calculate the hedging quantities of the Heston model. I undestand that the replicating portfolio consist of one option, $V = V(S,v,t)$, $\Delta$ stocks and $\phi$ units of the option to ...
2 votes
5 answers
858 views

Who hedges (more): options seller or options buyer?

When the open interest increases, this means that there is a buyer and a seller of that option. Both seller and buyer are behooved to hedge their positions, with the opposite sign; but I doubt that ...
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If you continuously delta hedge a long option position will you be flat at expiry regardless of realized vol? [closed]

Learning about gamma and am confused about practical gamma trading strategies and struggling to understand how they can be monetized. Is all gamma just about setting limit orders above and below and ...
5 votes
2 answers
735 views

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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3 answers
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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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How do sell-side institutions manage interest rate derivatives books in practice?

I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
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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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1 answer
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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 ...
2 votes
1 answer
177 views

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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131 views

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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2 answers
441 views

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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1 answer
602 views

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 ...
3 votes
1 answer
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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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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 ...
7 votes
3 answers
868 views

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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191 views

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 ...
2 votes
1 answer
217 views

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 ...
3 votes
1 answer
590 views

Optimal Hedging of Options - asymmetry between long and short vol positions

Going over Zakamouline's Approximation method for optimal delta hedging of options, it is claimed that the result remains valid for both buying options (long vol positions) or selling options (short ...
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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 ...
-2 votes
1 answer
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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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1 answer
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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% ...
2 votes
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210 views

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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218 views

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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584 views

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 ...
4 votes
1 answer
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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. ...
5 votes
1 answer
5k views

How can one value a Bermudan option?

A Bermudan option allows early exercise at predefined dates, e.g. at maturity equal to $t_1$, $t_2$, $t_3$,...; hence , would its value be the sum of 3 discounted European options with 1-year ...
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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 ...
1 vote
2 answers
1k views

FX hedging: forward rate and implied forward rate

In this paper (box 1 page 24): https://www.rbnz.govt.nz/-/media/ReserveBank/Files/Publications/Bulletins/2000/2000mar63-1brookeshargreaveslucaswhite.pdf It is argued that the forward rate that a ...
6 votes
2 answers
12k views

How to Delta Hedge with Futures?

The theory of delta hedging a short position in an option is based on trades in the stock and cash, i.e. I get the option premium and take positions in the stock and cash. In the classical no-...
1 vote
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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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1 answer
1k views

Bond Hedging: PCA and regression based hedge ratios

This is my first question and I would very much appreciate any help. For a project I am trying to compare different hedging techniques for hedging a long portfolio of bonds. I have a history of ...
1 vote
1 answer
385 views

Hedging a long position-one period from Steven Shreve Stochastic Calculus for Finance

The following question is taken from Steven Shreve Volume 1, Chapter 1, Exercise $1.6$ (Hedging a long position-one period) Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $...
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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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443 views

Delta hedging for an American call option on a stock with a continuous dividend yield

Let the dividend yield be $\delta$ and $C_u, C_d$ and $S_u, S_d$ be the up and down values for the stock and the call respectively over the period $\Delta t$. In Hull and all other resources I've ...
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2 answers
2k views

Hedge backtesting: ex-ante Beta vs observed Beta (is this even possible?)

A global equity portfolio has for objective to outperform a benchmark (MSCI World). I hedge the sensitivity of the portfolio to MSCI World (the beta) so that only the alpha remains unhedged. The ex-...
4 votes
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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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