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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How to estimate or determine leverage from strike price on ITM call option? [closed]

In this text 4x leverage is mentioned: "ITM call options have a strike (X) below spot price (S). ITM call option position is determined by aiming for ~4x leverage. The position size is set at 33%...
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Where can I find statistics of options? [duplicate]

I am a beginner into the options world, I am reading Paul Wilmott's book (Paul Wilmott Introducing Quantitative Finance) and trying to plot the models he derives on charts. I am also a programmer, so ...
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Why IV surface over call price surface? [closed]

Why do options traders usually model and trade the IV surface? I appreciate that the IV surface is more standard across assets, but why do we go to so much trouble with the IV surface? To me it seems ...
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How to fInd relation between call and Put IV on expiry day without calculating?

During the expiry day, in the European style options, the effect of rho will be very less. Let on expiry day the market is exactly at some strike price S at some moment of time. At that moment if the ...
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Contradictory arguments for ATM/ITM/OTM option demand

I am trying to understand which of the options have the most demand, and found this discussion here. The arguments presented are as follows: ATM is more liquidly traded than ITM/OTM because they are ...
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Stopping times, question on exercise

I'm completing exercises from Steve Shreve - Stochastic Calculus for Finance I and I'm stuck on one subtask for which I can't find missing element for 11 stopping ...
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Model based PnL explain for FX Options

In FX options the vol surface for a given maturity is usually described by three or five points, I.e. Atm, 25 delta risk reversal and butterfly and 10 delta risk reversal and butterfly. Then models ...
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How to determine break-even price on a delta hedge?

Suppose there is a portfolio of short $x$ shares and long 1 call option. This call option has a strike and premium. If the stock moves up, you loss money on the short position but gain on the option ...
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Black and scholes option pricing

I have to solve the following problem in the Black and scholes model: find the price at anty $t\in[0,T)$ for an option whose payoff at the maturity is: \begin{equation} 0 \ \ \ \text{if} \ S_T<K_1\\...
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In the derivation of the Black-Scholes PDE, using delta hedging, how is this linked to the risk neutral valuation? [closed]

I was reading this paper: http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf I don't understand the paragraph here: "The most interesting feature of the Black-Scholes PDE (8) is that ...
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Why should delta-neutral backspread always result in credit?

Natenberg mentions in chapter titled "Volatility Spreads" : under the assumptions of a traditional theoretical pricing model, a delta-neutral ratio spread where more options are purchased ...
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Pricing Leveraged ETF option based on base ETF

I am following along with the paper linked here: https://math.nyu.edu/~avellane/thesis_Zhang.pdf . In section 4.4, equation (4.4.2) makes the claim: $$\sigma(k) = |\beta|\sigma_s(S_0k^*)$$ where: $$...
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Convert implied probability into real probability

In this article I have read that: A risk-neutral world is one where all investors are indifferent to risk and don’t require any extra risk premium for the risk they bear. In this world, all assets (...
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When calculating VIX, how to deal with the problem of asymmetry of put and call data?

I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the ...
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Vanna vs volga and vega

So the bloomberg article that I'm referring to (Bloomberg. Variations on the Vanna-Volga Adjustment. Travis Fisher. Quantitative Research and Development, FX Team. January 26, Version 1) states that ...
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Why is my put intrinsic value greater than my actual put value in BSM? Python code

I have been creating a class for determining put/call values based on the Black Scholes Merton model and have run into a weird problem. For some reason my put values end up being less than the ...
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Why do bonds with a shorter next call dates have shorter extension risk?

I was reading a research article and I'm not really understanding why. Is it to do with the option premium being priced in at the beginning?
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Understanding EEX Futures and Options

I'm interested in understanding more about the European Energy Exchange (EEX). In particular, I am focusing on the energy option market and I would like to understand how vanilla options are quoted (i....
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What is the market standard for IR option pricing when moving to SOFR

From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM). But LMM models the forward LIBOR rate. What will happen to it once LIBOR ...
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Value at Risk on equity options, what is the right approach on historical simulations

Questions on Historical VaR for options, how do you actually do this. how you would evaluate Value-at-Risk for an equity option that has been recently listed on the exchange. The obvious is that you ...
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Why do companies trade options?

Companies buy options to reduce the variability in future cash flows. Institutional investors invest in portfolios to maximize return for a fixed amount of risk. If an investor owns stock in company A ...
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Derivations of the pricing PDE for the Heston-Hull-White or Heston-CIR models

Consider the hybrid model given by $$dS=(r-q) S dt + \sqrt{v} S dZ_1$$ $$dv = \kappa_v (\theta_v - v) dt + \sigma_v \sqrt{v} dZ_2$$ $$dr = \kappa_r (\theta_r - r) dt + \sigma_r r^p dZ_3$$ with ...
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Does Put-Call parity have influence over American Option pricing in practice?

I am learning my options and from what I read it seems that put-call parity is regarded as only being applicable to European options because the time to exercise is known. American options, on the ...
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Can I use the QuantLib Monte Carlo engine to price American options using heavy/fat tailed-distributed random numbers?

This might be silly, but I’m seeking to use QuantLib to price vanilla American call and put options using a Black-Scholes-Merton process and the Monte Carlo pricing engine based on the Longstaff ...
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Should we use the conditional expectation to write the value of an option?

So, I've just started looking into financial mathematics and the following question keeps bugging me. From what I understood, if the market is arbitrage-free and a given contingent claim of value $h$ ...
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Why is this inequality strict for arbitrage argument for European call?

in the notes about arbitrage arguments I am reading, I notice the statement We can also see that $$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$ Notice that the inequality holds STRICTLY! I don't ...
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get all trades on option chain from a day

I would like to collect all trades from a day on option chain. Aggregate last price&size to calculate dealer positioning. Is it possible to collect these from a stream taking ...
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What are some good books to get started with option theory? [duplicate]

Recently graduated in econometrics but starting to realize my knowledge is limited. Any and all tips are welcome!
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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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option pricing using empirical distribution

I am looking for ways to express a directional bet on a commodity through futures options. Assume that there's 50% probability that oil will spike up 100% in the span of 30% during the next 9 months ...
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How do I extract the arbitrage?

You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments: Each unit of stock is priced at \$10. A call on the stock with ...
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Pricing FX options on pegged currencies

I'm wondering what's the standard (if any) for practitioners to trade volatility on pegged currencies. Is there any specific convention? I'm thinking situations like EURCHF before the unpeg, how were ...
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1 vote
1 answer
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Difference between closed form binomial option value and monte carlo simulation

I am trying to calculate the price of a European call option using both the the closed form expression and a monte carlo simulation. But the value's I get from both these methods are not the same: ...
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Stress scenarios for Down In Put (DIP)

I am preparing stress scenarios for long Down In Puts (e.g -10%,-15% drop in underlying equity price). I assume that the maximum delta hedge is 300% for DIPs with barrier levels within 0%-5% ...
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Can the Feynman-Kac formula be used for asset classes that don’t have options?

So rather than a call option C(S_t,t) we have some type of asset with asset price is given by S(x,t) where x is any type of variable that the asset price depends on. I.e Price of wooden desks, W(x,t) ...
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5 votes
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Implied volatility of Asian options under Black76 model

I found this repository (options pricing in Python) where they adjust IV for Asian options and they use it under the regular BS76 model. I could not find any proof of this result on the web, do you ...
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The use of the trading time variance/volatility curve

In trading, how is the trading time variance/volatility curve and spread curve such as depicted and parameterized on p. 277 of Jim Gatheral and Roel C.A. Oomen, Zero-intelligence realized variance ...
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European option with payoff $X_T^2$ [closed]

I have been ask to price a European option with payoff $H(X_T,T) = X_T^2$ using the equivalent martingale measure (EMM). For this I used the process: \begin{equation} dX_t = r X_t dt + \sigma X_t d\...
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Options market: quote-driven or order-driven?

In my understanding: bonds, currencies, and commodities (cash, not derivatives) are traded in a quote driven market with a market maker who "will either fill your order from its inventory or ...
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Option Extrinsic value representation [closed]

The typical representation of the extrinsic value of an option is the following: Is the gaussian the real representation of extrinsic value derived from Black and Scholes? Should it be lognormal? ...
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How an Option market-makers make money?

This might be a very broad question, but I would like if someone can please explain to me how a market makers make money in Options market ? Thank you
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B&S pricing of option with convex transformation

Assuming B&S world, is it possible to price an (European) option on a general transformation $f(\cdot)$ of $X$? What kind of assumptions should we make on $f$? Is convexity sufficient to find some ...
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Modelling forward and correlation dynamics for options on the best-of multiple commodity spreads

I am looking at best-of options on futures (commodities), let's take for example the following payoff specification: $ max(a_{1}-c_{1}, \ a_{2}-c_{1}, \ a_{3}-c_{1}, \ b_{1}-c_{1}, \ b_{2}-c_{1}, \ ...
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Options Market making, what to do with ITM options

I am a option market maker. Say at some point in the time, I end up having only but ITM options in my portfolio and I want to reduce my risk exposure ( delta, Vega, gamma), what can I do to make ...
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Weekly S&P500 options price data

I cannot find free data on S&P500 options price, call and put, at different strikes of weekly options, on a daily basis, with maximum and minimum prices. I would like to have this data to study it....
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1 vote
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The option is "purer" in its risk---what is meant by this?

In the book "The Concepts and Practice of Mathematical Finance" author M. Joshi writes on page 12 the following: "From the point of view of risk, we can regard an option as an attempt ...
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Option's Delta Investopedia Question

New to this. In this Investopedia article on Delta the following looks like a typo - How Do Options Traders Use Delta? Delta is used by options traders in several ways. First, it tells them their ...
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What do "heating degree day" prices actually measure?

The futures for Dallas Heating Degree days for July 2022 are trading around 6.83 But Dallas is hot in July and does not typically get any heating degree days So, what does the 6.83 for July 2022 ...
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2 votes
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Pricing Options on Inefficient/Illiquid Assets

I'm currently trying to gather more information on option pricing in very inefficient markets for the underlying. By inefficient, I mean markets with consequential bid-ask spreads (5% or more) and ...
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When is the gamma of an iron butterfly spread positive? (Assuming stock price at t=0 is equal to the highest strike price)

I know the Gamma of a butterfly using calls is $$\Gamma_{butterfly} = \Gamma_{C_{K_3}}-2\Gamma_{C_{K_3}}+\Gamma_{C_{K_3}}$$ Where K3-K2 are the same as K2-K1 and S=K1, But under what condition is the ...
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