Questions tagged [hedging]
Financial strategy used to offset potential monetary losses or volatility.
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Hedging FX Risk of a fund
I manage a mutual fund where the underlying assets (or the shares i buys) are in USD, and my mutual fund is in CLP (Chilean Pesos). How can i hedge this fx risk without affecting the return of the ...
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Any other ways to hedge a bond portfolio against interest rate risk? [closed]
I'm currently taking a (gentle) intro to derivatives class. One of the exercises asked me to discuss duration as a risk measure and to provide alternative methods of hedging a bond portfolio against ...
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Delta Gamma Hedging Portfolio of Multiple Options Derivation
I am trying to make the correct derivation of the Delta Gamma Hedge of a portfolio composed of a multi-option strategy, like a Straddle with the following parameters Long 1 Call K = 100, Long 1 Put K =...
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Delta hedge call option on short rate
Usually delta hedging an european call option in the black-scholes model is constructed of three assets; a call option, the underlying stock and the risk-free asset often assumed to have constant ...
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Backtesting One-Factor HJM model with selling European Receiver Swaption
I am attempting back test the performance of a model - namely the Musiela equation used to model instantaneous forward rates with constant time to maturity:
$$r(t,x)=r(0,x)+\int_0^t\left(\frac{\...
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equities hedging betas for a cross-sectional risk model
This question is on equities risk models. I would like to know how to define betas when using a cross-sectional regression approach, rather than the time series approach. My goal is beta hedging of a ...
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In a CRR model, find the Initial investment of the hedging strategy
Given a Cox-Ross-Rubinstein model with $T=10$, $u=1.1$, $d=0.9$,
$r=0.02$, $S_0=100$ and a European call option with Strike $K=220$,
find the initial investment of the hedging strategy.
I know how to ...
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Relationship between options open interest and spot price movement
The hypothesis that I am mulling over (and more so, its effect on stock price movement) is the following.
Hypothesis: Buyers of options do not hedge (as they don't need to) while sellers usually hedge ...
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Where can I learn more about market-making strategies? [duplicate]
I have some experience trading both sides of an order book, but not simultaneously in the same security (and certainly not at the size large market makers do.)
I've searched pretty extensively for ...
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What is your exposure when you sell a binary option
I recently made a post that was closed right away because it wasn't focused and asked too many questions. In that post, I asked five questions that were related but different. It looks like stack ...
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Where am I going wrong with the calculation of conitnuous PnL from delta hedging?
I am trying to work out the PnL of continuous delta hedging. I saw This link to an answer here, however, I obtained a different answer without resorting to Black Scholes, which I will outline below.
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Dynamic Hedging
I am reading page 126 (Chapter 8) of the book "Option Volatility and Pricing 2E" by Sheldon Natenberg and have two questions I seem to be stumped on. (The bulleted text below the charts in ...
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Should one use the 30y bond alongside shorter tenors to hedge a MBS book?
Say I build a US treasury curve or swap by bootstrapping 2/3/5/7/10/20/30y on the run bonds. Say I have a prepayment model and an OAS model and I can generate key rate dv01s for the book as dBookNPV / ...
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Why reduce number of short contracts to reduce beta, and take long positions to increase it?
My question is about chapter 3 in the ninth edition of "Options, futures and other derivatives" by John C. Hull, subchapter 5 under the heading "Changing the Beta of a Portfolio".
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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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Conditions for market completeness
We know that a market is called complete if it is possible to replicate any future payoff trading in its securities. Is there an exhaustive list of requirements that when satisfied imply market ...
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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 ...
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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 ...
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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 ...
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Replicating strategy for the zero-coupon bond in the Hull-White model
I would like to derive a self-financing, replicating strategy for a call option on a zero-coupon bond in the Hull-White model. I tried to use Proposition 21.10 in 1, in which zero-coupon bonds are ...
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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
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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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ETF Market Making Hedging
Suppose I am a market maker making a market on an S&P ETF. Suppose that I have calculated a fair ETF price of $395. My market therefore is 394.90 (bid) and 395.1 (ask). After my bid is posted I ...
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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 ...
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How to actually compute delta when delta hedging with a (time varying) volatility model?
I was reading some papers on delta hedging, many of which reference "Which Free Lunch Would You Like Today, Sir?" (Ahmad/Wilmott) which describes the following setup:
Quote option with $\...
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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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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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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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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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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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