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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Options market making process (step-by-step)
What are the steps involved in options market making?
Does it roughly follow this procedure:
Choose a pricing model, e.g. Black-Scholes.
Calibrate the model, e.g. Volatility.
Quote a bid-ask spread ...
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Volatility Surface Construction: Ask IV, Bid IV and Mid IV
I am presently engaged in a project wherein my objective is to construct a volatility surface utilizing either the SVI parameterization or the SABR model, leveraging real market data. Initially, I ...
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Empirical Evidence for Support/Resistance Levels in Martingale Price Processes and Its Impact on Option Volatility Surfaces
In financial mathematics, the martingale property often serves as an essential foundation for the stochastic processes that underlie securities pricing models. According to martingale theory, the most ...
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Optimal Fitting Criteria of SABR
I was reading about SABR Model and curious about this.
The process of fitting the SABR model involves finding values for the parameters α, β, ρ, ν that minimize the difference between model-implied ...
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Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?
I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model.
Firstly, why would it be ...
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Volatility Time and Interest Rate Time
In Sheldon Natenberg's book "Option Volatiliy & Pricing (2nd)", he mentioned that (on page 65), only trading days (roughly 252 in a year) are counted when computing vol time and all ...
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Can someone provide an example of how arbitrage would be used when an american call option can be bought for less than max(final stock - strike,0)? [closed]
"Final stock" means the stock price at expiration, and "strike" means strike price. If a call option had to be purchased for more than the max(final stock - strike,0)then you would ...
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Difference Between Option market price and Theoretical price? [closed]
So I am working on strategies that depends on the difference between Actual market price of option and price derived using black and scholes model.
For eg: Spot 19000 , strike 19200 . It is OTM call ...
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Modelling the Implied volatility of an asset
I want to estimate the implied volatility of an asset which has not historical implied volatility data. I do have the historical realized volatility ( I have the historical prices). What would be some ...
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Calculating the Delta of FX option
I'm tying to reconcile the delta value for an FX option. I'm comparing the results to Bloomberg to verify our calculation is correct.
I've looked at this - Quantlib: Greeks of FX option in Python but ...
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asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value
I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
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Dealer's directional open interest
This question is related to the previous question I asked here. In one of the answers, the article from Squeezemetrics that discusses the effect of GEX on the spot price of an asset was pointed out. ...
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Best Method (Or Just a Good Method) of Predicting Intraday Volatility in Real Time?
I apologize if this is a stupid question, I'm a complete neophyte in academic finance but I am trying to learn.
I am trying to create an estimate of how likely indexes are to rise/fall by x% by the ...
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Can the risk neutral pdf derived from Breeden-Litzenberger Method be used to calculate vega and theta?
I have been researching volatility smoothing techniques and risk-neutral pdf.
I noticed one interesting post in
Does the risk neutral pdf that is derived using Litzenberger-Breeden Method correspond ...
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systematic trading reading fixed income [closed]
I would like to expand my knowledge on systematic strategies in fixed income. I know there are a lot of articles on equity but these markets are different and I would like to know more. Are there good ...
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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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computing implied volatility from greeks
Given a set of greeks (delta, gamma, theta, vanna, volga, vega, rho) and other information such as the dividend rate, dividend forecast, and realized volatility for American or European Options but no ...
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Accounting of a stock put option for Monthly % Changes
am looking to backtest a strategy of systemic put buying on an equity index (e.g SPX Index) so say a strategy of buying 1Y 90% SPX Puts rolled 1 day prior to expiry.
As opposed to only calculating the ...
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Option Payoff in Different Currencies
In the stackexchange answer Change of numeraire in options with currency exchange features
Pratically speaking, what this expresses is that these two things are the same:
Converting the payoff (which ...
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What is your preferred API/source for historic futures (ES) options pricing data and if possible, the Greeks? [duplicate]
Crowdsource question: What is your preferred API/source for historic futures (ES) options pricing data for the greeks? (NOTE: Over ten years ago, there was a similar question with several suggestions, ...
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QuantLib: Analytical Greeks and Numerical Greeks do not match?
I use the Black Scholes Merton (BSM) model from QuantLib to calculate Call options price and its analytical Greeks. I also manually calculate its Numerical Greeks (Theta, Vega), but the results do not ...
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Pricing an American FX Option using Quantlib
I need some guidance on valuing American style FX options (spots and forwards) using quantlib in Python. Given the following parameters:
Domestic and foreign risk-free rates
Current market spot and ...
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Conventions and Modeling of CDS Options
I am curious about the current standard conventions and modeling techniques in the CDS options market. I would be glad if someone could elaborate on the following topics:
State of the art of index ...
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Covariance Matrix of Correlated Random Variable
Suppose I know or have estimated the covariance matrix for one random variable (for example an asset) and have:
$$
\begin{bmatrix}
<\text{spot, spot}> & <\text{atmv, spot}> \\
<\...
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How to apply put-call parity in volatility surface construction?
How to make the volatility surface free of put-call parity arbitrage? If I bootstrapped the implied vol from a call price and plugged it into the BS model to have a put price, what if it violates the ...
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Cost of Delta Hedging
I am confused about the following question:
A trader holds a portfolio of short option positions. The trader limits the risk of these exposures by maintaining a delta hedging strategy. In evaluating ...
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How does the inclusion of stochastic volatility in option pricing models impact the valuation of exotic options?
Been lurking this forum for quite some time and there’s this concept I can’t wrap my head around:
How does the inclusion of stochastic volatility in option pricing models impact the valuation of ...
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Filtering options data
I am looking to conduct some analytics with regards to options implied volatility. My advisor mentioned about filtering options with time to maturity of less than 7 calendar days. Is there a ...
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When is gamma and theta in the same direction?
So, I am reading Natenberg and it says that during expiration(close to expiration), the deep in the money options will have Gamma and Theta in the same direction. This was a bit counter intuitive to ...
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Basic option question - spx implied move per day in points
I know that an option implied move per day is vol/sqrt(252).
That being said if I want to convert this in actual SPX points, am I just supposed to multiply this by the forward ? I've been told a 2/...
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Typical values Heston parameters for FX options
I am not as familiar with FX options as I am with equity index options.
For the purposes of numerical testing/experiments I'd appreciate if somebody could tell me what are typical parameter values for ...
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SPX AM vs PM Reg T (T+1) Cash Settlement Dates
Assuming I have two SPX options expiring the third Friday of a normal month with no holidays around. One (SPX) option has an AM settlement while the other (SPXW) has a PM settlement. The last trading ...
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Quantitative trading strategies with a focus on low-frequency dislocations
I am looking for references that are specific to quantitative trading strategies that exploit low-frequency dislocations in markets, which lend themselves as overlays for a strategic asset allocation ...
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Computing moments of implied distribution
For simplicity let's assume that the discount rate $r = 0$, then a price of a call option with strike $K$ and maturity $T$ on an asset with positive price can be computed as $C(K) = \Bbb E_Q(S_T-K)^+$....
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Can you trade options with market scoring rules?
In a double-auction market, buyers and sellers are always balanced in number -- a traditional market-maker in such markets doesn't really hold any assets/take any position long-term.
However, with a ...
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CBOE Option Sentiment alternative datasource [duplicate]
I am interested in CBOEs Option Sentiment data (https://datashop.cboe.com/option-sentiment)
It contains high level (aggregated) Options data on a daily basis delivered in a csv file. Main Datafields:...
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Why are option bid and ask option prices aggregated by 0.05
I noticed, that the option prices below strike for call and above strike for put options always end with 5 or 0. I tried placing my order with a price of 0.01 above the bid, but I haven't seen it in ...
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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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Options strategy expiration probability
Big picture
For any options strategy, for any segment between zero profit (breakeven) points, I want to calculate probabilities of the underlying instrument price will be within a segment at ...
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How to replicate a claim in a stochastic volatility model?
Given a Markovian stochastic volatility model with an asset $S$ and a variance process $V$ given by
$$
dS_t = \mu_t S_tdt + \sqrt{V_t}S_tdW_t, \\
dV_t = \alpha(S_t,V_t,t)dt + \eta \beta(S_t,V_t,t)\...
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Optimal delta-hedging frequency when gamma scalping
Is there a practical way to calculate a delta threshold for rebalancing when gamma scalping?
I know it does not effect expected P&L, but what about optimizing for P&L sharpe ratio after ...
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Calculating skew for an options structure
I am trying to figure out whether an options structure is short or long skew without just having someone tell me the answer. I'd like to calculate the number myself. Assuming I am creating a risk ...
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Derivatives without analytic expressions? [closed]
I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo ...
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Homogeneity of BS Formula
I'm reading M. S. Joshi's paper "Log-Type Models, Homogeneity of Option Prices and Convexity", and I'm having problem understanding equation 1:
$$
C(S_0, K) = \int (S - K)_+ \Phi\left(\frac{...
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Input/References on Generating Exit Signals for Positions that Profit Very Highly from Extreme and "Unpredictable" Events?
For focus, let us restrict the scope of this to vanilla options-based positions/strategies.
In a lot of the accounts that I've seen of those that engage in this sort of investment/trading strategy (...
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SABR: how to deal with the wings?
I have experimented a bit with the SABR model. In particular I have calibrated it on EURUSD. Obviously, as SABR is a 3 parameter model, it will not fit the 5 market quotes consisting of ATM, 25 delta ...
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How to fit (find $u$) in the binomial options pricing model?
In the binomial tree options pricing literature, I see frequent reference to the definition that
$$
u = e^{\sigma \sqrt{n/t}}
$$
I think I understand the model, but how do we derive this, i.e. how do ...
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Implied Volatility Discrepancy in American Options - Mathematical Reasoning?
I've been analyzing Tesla stock American options data and have observed an interesting pattern that I'd appreciate some help understanding.
For this analysis, I obtained the Implied Volatilities (IVs) ...
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Black-Scholes formula is a (probabilistic) convex combination
[![enter image description here][1]][1]A call price is bounded when $\sigma\sqrt{T}$ goes to $0$ and $\infty $ by:
$$C_{inf} = e^{-rT}[F-K] \leq C \leq C_{sup}=S $$
Now a simple rearrangement of Black-...
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Methods for tracking option open interest intraday
It is my understanding that open interest option values on financial websites are a reflection of a snapshot value each day. Is anyone aware of methods for estimating intraday open interest, or aware ...
