Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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2answers
127 views

How to derive Black-Scholes equation with dividend?

Question: The Black-Scholes equation without dividend is given by $$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS \frac{\partial V}{\partial S} -rV = ...
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42 views

How To Calculate The Implied One Day Expected Return For Earnings

I am trying to figure out how to calculate the one day expected return given I have the event volatility. In his book Trading Volatility, Correlation, Term Structure and Skew, Collin Bennet (link) ...
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36 views

Is my derivation of Black-Scholes equation correct or am I missing something (eg assumption)?

Question: The following is my derivation of the Black-Scholes equation. Is it correct or am I missing some details (eg assumption)? Let $V$ be value of an option. Suppose value $\Pi$ of a portfolio ...
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3answers
140 views

Explain that gamma is positive for standard call and put options without using heavy mathematics

Gamma is positive for any standard put and call options seems like a standard fact. A proof can be found in this post. However, the answer provided in that post involves heavy mathematics. Is ...
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1answer
447 views

Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
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1answer
48 views

Compute Vega and Delta in R

I am trying to compute greeks for a large sample of CEO compensation contracts in R. However, my vega computations all result in a value of zero. In doing so, I follow Core and Guay [2002]: Here is ...
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1answer
47 views

HEDGING WITH A PUT OPTION

In the following example, for 3rd question and 4th question why do we have to add (Stock price in three months - Current stock price) to put option profit? Thank you in advance.
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15 views

Applications of a calibrated price or IV surface and other basic questions

Newbie here with basic questions. I have researched the topic online, but am still at a loss. I went through a nice course on calibration, saw how to apply stochastic short rate, stochastic vol, jump ...
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1answer
42 views

Do not understand 'The gain (loss) on the stock position would then tend to offset the loss (gain) on the option position' [closed]

Currently, I am reading John Hull's Options, Futures and Other Derivatives. On page 401, the author mentions the following: Suppose that the delta of a call option on a stock is $0.6$, stock price ...
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1answer
105 views

Duan (1995) GARCH Option Pricing Model with MATLAB

This is the MATLAB code that replicates the option pricing model proposed by Duan in his paper "The GARCH Option Pricing Model". However, the parameters estimated in the file do not match with the ...
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1answer
63 views

If the volatility is zero (i.e. σ=0), what is the call worth? After valuing the call, how to hedge the call (assuming you sold it)

Question: All Black-Scholes assumptions hold. Assume no dividends. The stock price is $100. The riskless interest rate is 5% per annum. Consider a one-year European call option struck at-the-money (i....
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19 views

American Option - Early exercise risk management

This is for American Option Book Management in real trading. Let`s suppose, American Option seller(Book manager) only do delta hedging, which means seller cannot do Vega hedging, American Option ...
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1answer
171 views

Implied interest rate using put-call parity

In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end. I want to ...
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32 views

relationship between option vol and option payoff

Has anyone thought of the relationship between the option vol and distribution of option payoff? for example, I have 1000 paths of simulated underlying prices, keeping all inputs the same but only ...
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1answer
44 views

Why would a lower stock price leads to higher value of a call option?

Currently I am reading Basic Black Scholes: Option Pricing and Trading by Timothy Falcon Crack. At page $47,$ the author mentions the following. Higher interest rates decrease the present value of ...
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1answer
25 views

Do not understand 'If an option position includes short American-style options, then the payoff-diagram may be misleading'

Currently I am reading Basic Black Scholes: Option Pricing and Trading by Timothy Falcon Crack. At page $42,$ the author mentions the following. If an option position includes short American-style ...
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1answer
45 views

<Credit Default Swap> Auction Recovery vs Fixed Recovery

What is the Difference between Auction Recovery CDS and Fixed Recovery CDS?
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54 views

Optimizing monte carlo code in python [closed]

What are they key points to use while coding a monte carlo simulation in python? I have the following monte carlo code : ...
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0answers
56 views

What is the name of these digital basket options?

Consider a basket of correlated assets $(S_1(t),\ldots, S_N(t))$, as well as a vector of strike prices $(K_1,\ldots,K_N)$, and let's look at the following European payoff types: An option that pays 1€...
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1answer
153 views

When would open interest equal trading volume?

I know the difference between open interest and trading volume. Open interest is the number of contracts, long or short, outstanding. Trading volume is the number of contracts traded in a day. ...
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1answer
284 views

Options Market Making Used Implied Volatility Surface

Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In ...
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1answer
149 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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1answer
145 views

Implied volatility equality for deep in/out-of-the-money put and call

Someone posed the following question. Given a strike $K$ and the stock price $S$ and the same maturity are the implied volatilities of the call and put with these same parameters equal for $|S-K|\gg0$...
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1answer
71 views

Why and how is Implied volatility directly related to stock price but inversely related to strike price?

I know that in equity markets there is a volatility smirk which results in higher IV for lower strike price options because of crashophobia and leverage related factors but I can't wrap my head around ...
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82 views

Why would a buyer buy a Warrant vs an Option, both having the same economics

Assume you have a Warrant and an Option both with the same economics i.e strike, expiry, type etc. Also assume that the Warrant has been issued by a high grade reputed issuer (i.e there is a almost a ...
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440 views

Why risk neutral probabilities should be strictly greater than zero for no arbitrage condition?

I was recently told by a colleague that the risk neutral probabilities should ALWAYS be greater than zero to have a no arbitrage condition. Intuitively, we know probabilities cannot be < 0, but how ...
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2k views

Why a Target Redemption Forward cannot be used as hedging instrument?

A Target Redemption Forward (TARF) allows you to buy or sell foreign currency at an agreed “Enhanced Rate” for a number of expiry dates. But why can't a Target Redemption Forward (TARF) be used as a ...
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34 views

Procedure of model calibration

Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the ...
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0answers
54 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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1answer
61 views

Can someone provide a good definitive explanation for rho in relation to option risks?

I have a pretty good understanding of option risks except for one thing, rho. Unfortunately, interest rates tend to have a small effect on option prices, and thus most literature tend to just gloss ...
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1answer
53 views

SPX options strike bracket

By what rule does the CBOE determine the available strikes for puts and calls on the SPX? The contract specification (http://www.cboe.com/products/stock-index-options-spx-rut-msci-ftse/s-p-500-index-...
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1answer
71 views

If 10s20s steepener have equal DV01 weighting on each swap then why does convexity play a role in MtM

Receiver Swap 10yrs Notional: 1,000,000 DV01: +1,300 Tenor: 10yrs Rate: 4% Payer Swap 20yrs Notional: 500,000 DV01: -1,300 Tenor: 20yrs Rate: 5% Looking at this fictitious example, I want to ...
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195 views

Why does expected price of OTM option not equal to BS price?

If I assume that stock returns follow normal distribution with drift = 0% and S.D. = 10%. In the long, if I keep investing in this stock for a year with the same capital every year for a consecutive ...
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1answer
79 views

Why is the value of the Brownian motion bounded by the maximum value of this square difference?

This comes from Taleb and Madeka's paper (https://www.academia.edu/39998351/All_Roads_Lead_to_Quantitative_Finance_Response_to_Clayton_?auto=download) regarding arbitrage restrictions on binary ...
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1answer
250 views

What is the industry standard pricing model for CME-traded Eurodollar future (American) options?

The CME-traded Eurodollar futures option is an American option. What is the industry standard pricing model for this product? Does the industry practice to treat CME-traded Eurodollar futures ...
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7answers
8k views

When does delta hedging result in more risk?

A question from an interview book: When can hedging an options position make you take on more risk? The answer provided is the following: Hedging can increase your risk if you are forced to ...
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3answers
429 views

Why does buying future options require margin?

An option is the right, but not the privilege, to trade an underlying at the strike price. Buying a stock option doesn't require any margin - I've just tested this with InteractiveBrokers, trying to ...
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1answer
58 views

In literature, is IV constantly adjusted during option delta hedging?

In a lot of literature, they like to compare the performance of buying an option, and then delta hedging either at that options implied volatility (IV) or the true future volatility. This is under ...
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2answers
144 views

theoretical reason for which we can use monte carlo simulation for option pricing

The classic way to price an option is solving either analitically or numerically the associated PDE subject to the terminal and boundary conditions. An alternative approach is to use monte carlo ...
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4answers
283 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
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2answers
671 views

What are some beginner quantitative option trading strategies?

I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc). I would like to know if there are any basic quantitative option trading strategies that can ...
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0answers
80 views

Trading with S&P 500 options

Could someone help me who has experience with trading S&P 500 options? I am curious about any liquidity trends (if OTM, ATM, ITM are the most liquid, and with what kind of maturity), and the ...
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26 views

Is it possible to price a double barrier option which one barrier is monitored continuously while another barrier discretely without using MCS?

I am thinking about pricing a down-and-in and up-and-out double barrier put option under Black-Scholes assumption. The upper barrier is monitored continuously and the lower barrier is monitored ...
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5k views

Delta Neutral / Gamma Neutral Positions

I've been trying to find out more about options positions which are both delta neutral and gamma neutral--created with some kind of calendar spread. Supposedly, such a trade will be perfectly hedged ...
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2answers
289 views

How to hedge two currency positions

Having two spot currency positions, short EUR/USD long GBP/USD We are looking for a way to diminish the risk of the spread going against us. The basic idea is ...
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2answers
531 views

Leveraged Permanent Portfolio Using ITM Call Options

The permanent portfolio proposed by Harry Browne has had an excellent track record since the 1970's. It is able to compound at roughly 8% annually with a Sharpe ratio around 0.7. The permanent ...
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0answers
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Vol surface fitting to options on commodity futures

Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage. I think the ...
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Hedging Strategies involving Forwards and Options [closed]

"An investor or business with long exposure to an asset can hedge exposure by either entering into a short futures contract or by buying a put option. An investor or business with a short exposure to ...
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1answer
71 views

Hedging an option on a non-traded asset in BS world

I have given the following task given. Suppose you are in a Black-Scholes World where you have the standard assets $$ dS_t = \mu S_t dt + \sigma S_t dW_t $$ $$ dB_t = r B_t dt $$ and now you also ...