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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Delta of FX Options, Different Currency in Trading Book - Trading Interview Question

Having done stochastic analysis in university, together with tons of other math courses, do never prepare you for an actual interview in trading. Stumbled on what I believe might be an easy question, ...
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Monte Carlo: How to interpolate Dupire's Local Volatility

I am trying to price barrier options which can have daily or monthly observations. I first calibrated by Black vols into smooth SVI vols (with linear interpolation along time in variance) to obtain ...
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Calculate options prices based on given options and spread prices

Suppose you know the following information: Futures price on a stock is 66 70 strike straddle is trading at 27 50-60 put spread is trading at 2.5 50-60-70 put butterfly is trading at 0.2 Assume ...
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Backtesting Hedged Equity Portfolio with Options

I am trying to find some papers and methodologies on backtesting an Equity portfolio with broad-based index options as hedge. For example, take SPY and systematically hedge it with 9 months 30 delta ...
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Evaluating swaptions with negative interest rates

Does anyone know if it is possible to evaluate swaptions with negative interest rates with Quantlib? ...
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Is it true that interest rates options with different maturities are free of calendar arbitrage because of the different underlying rates dynamics?

The title says it all - is it true that European style interest rates options (lets say on LIBOR 3M for the sake of simplicity) with different maturities are free of calendar arbitrage because ...
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Black Scholes derivation: Why treat Delta as a constant?

In the derivation of the Black-Scholes equation, it is argued (e.g. in the original paper and in Hull) that $$dV(S_t, t)=(…)dt + \frac{\partial V}{\partial S} dS_t,$$ where $V(S_t, t)$ is the value at ...
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What is the TBA Option price convention and delta

I am wondering about price and delta about TBA options Use this trade example: One sell \$100 million ATM forward calls on 6.5% Fannie Maes for 24 ticks, and buy \$50 million ATM forward calls on ten-...
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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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Optimize call option purchase

If it is predicted that the price of a stock will increase from P1 to between P2 and P3 in time T (assume the distribution of the price will be evenly distributed between the range of [P2, P3] at time ...
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Distribution of total delta of option portfolio

We know the delta of a portfolio of options is simply the sum of deltas of the individual options. But are there any additional known properties about the total delta (or other greeks) of a portfolio ...
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Difference between number of stocks and number of bonds: Predictable vs adapted

Let $\nu_k$ and $\eta_k$ denote the number of stocks and number of bonds in the portfolio. According to Schweizer, we need $\nu_k$ to be predictable and $\eta_k$ to be adapted. In the text, the ...
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No-arbitrage conditions on a caps/floors volatility surface

Suppose that one has a caps/floors volatility surface and wants to check whether this surface admits arbitrage. What is the theoretical and practical way to do it? Lets talk only about caps for ...
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Difference between Risk minimization and local risk minimization

According to the survey paper "A Guided Tour through Quadratic Hedging Approaches" by Schweizer the risk function is defined by $$R_t(\phi)=E[(C_T(\phi)-C_t(\phi))^2|\mathcal{F}_t]$$ When ...
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Why can’t delta’s be used to price double no touch options?

Here is the link to a MATLAB one touch option pricing calculator I used:OT I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...
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Find the value of put option using a two-period binomial model

I've been asked to find the price of a two-month European Put Option with strike price $£40$. The price at $S_0=£30$, this can move up to $£40$ or down to $£25$ ($1/3$ chance to go up, $2/3$ chance to ...
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Power options for pricing European claims

I have the following question: Why would somebody be interested in the expression $E[S^\theta]$ for $\theta$ between zero and one. The only thing I know is that this then can be somehow used to ...
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Approximating Volatility Skew From historic returns? [closed]

I was wondering if someone could help me with something. I've been reading more about equity options, and I'm struggling with skew. Conceptually I understand why it exists, what I'm struggling with is ...
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How to find probabilities of moves in a trinomial tree?

I'm given a non-dividend stock with price $p$ and volatility $v$ and given a European Call option corresponding to this stock. I want to calculate the probabilities of the following moves: $M_U = \...
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Generating Greeks with American Options

Investor and Software Engineer but very new to quant finance here... I have the below code (which I'm sure will be helpful for some) and have some questions regarding the function parameters! Is RF ...
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Possible to Pull Individual Option Purchases through YFinance/Script?

I am trying to pull live trade data through python using yfinance, however, I cannot seem to find any sort of command that can output physical purchases of options (ex. one person purchased 4 call ...
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No Probability in Greeks

In an interview, I was once told that I should not consider probability when talking about option greeks since from a mathematical point of view greeks have nothing to do with probability. That is of ...
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Option pricing with risk-neutral approach

Problem Given $Y_t$ price of a stock (no-dividents), and a derivative paying $Y_T^2$ at maturity $T$, evaluate the price of the instrument now using risk-neutral approach and check that it satisfies ...
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Easy, but doubts - Annualize daily turnover

I am fairly certain I am correct but I just want to double-check on portfolio turnover calculation. I need to annualize the daily turnover rate. To calculate, the daily turnover, I am using the ...
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Greeks of portfolio in response to underlying price change

I'm trying to wrap my head around Greeks, and I'm getting a little bit confused. For example, let's say my portfolio holds a long 5 month ATM call with strike \$20, and short 2 month OTM call with ...
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CDS Option Pricing (Missing Index Factor)

I've read the OpenGamma paper https://quant.opengamma.io/CDS-Options-OpenGamma.pdf on CDS Options, and noticed a small discrepancy. So I wanted to double-check my understanding. In Section 6.4 the ...
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Can gamma of an option be greater than its delta?

I have a currency pair usdinr put option with strike price at 73.5 INR, risk free rate 0, underlying price of 75.4025, days to expiry is 15 and iv is 5.9%. Delta of this option is -0.019 and gamma is ...
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What is the greatest theoretical delta value?

In a few options positions I'm currently holding I noticed delta values of ~0.6 while gamma is ~1.0 which surprised me as I thought delta can never be greater than 1 - meaning for every 1\$ move in ...
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Arithmetic Asian options on two commodities

I am pricing a November-December Asian option on steel via Monte Carlo simulation. I intend to simulate daily prices for the Nov contract from today through end of November, and from today through end ...
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Optimizing Options Portfolio

I’m working on a model which creates a portfolio of options. The model has an alpha from an options trade for 1 period using several different underlying stocks. Would Mean Variance optimization still ...
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Why is call option value same as portfolio value at all times in Black Scholes model?

Following is a part of the text from Steven Shreve Stochastic Calculus for Finance II, for pricing the European Option in Black Scholes model. The argument is that today I start by selling a European ...
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Why are options studied separately from a portfolio of stocks and bonds?

I have just started studying finance and stochastic calculus so apologies if this question is too naive. I was first introduced to stocks and bonds as risk and riskless investment assets. Then a new ...
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Cash less exercise and redemption feature in SPAC warrants

Public and private warrants of a SPAC post merger (Initial Business Combination or IBC) are often very similar. Notable differences are 1) cashless exercise of the private warrants and 2) redemption ...
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Why doesn't the value of an in-the-money option increase approaching expiration? [closed]

I know it is a pretty basic question and I can get this result with BS, however I don't understand it conceptually. As the time approaches maturity, it is less likely to end out of the money, so I ...
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What are the different payments in a callable spread option? how is it structured

I encountered a product that's called CSO (Callable Spread Option). I would like to understand how this product works and how the payments are done in both ways? what about the callability of the ...
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What is the cause of this option chain anomaly?

LAST CHG BID   ASK VOL OPEN INT. STRIKE 363.15   1.35    359.80      361.40    6          12          420.00 What's peculiar is that the price is significantly higher than the ask price. The question ...
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Option Pricing - Incorrect price outcome for Out of the Money (OTM) calls

I have the options data for a stock - ...
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Early expiry options/deconvolution

Take a standard Markov setting (with assumptions as needed) $$ dX_t = \mu(t,X_t)dt + \sigma(t,X_t) dW_t $$ Assume, you can get the distribution (i.e. option prices) for $t_1$ (the early expiry) and $...
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Selling American calls before ex date vs. exercising

From reading Hull OFOD (among other references), I understand that early exercise makes sense for an American call option at time $t_n$ when $$D_n > K\Big[1-e^{-r\big(T-t_n\big)}\Big]$$ for a call ...
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Deriving Bachelier Greeks

I am working on the Bachelier Model with r not equal to 0 as described in the first and most upvoted answer in following link: Bachelier model call option pricing formula This is fairly easy to code ...
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is implied volatility derived from the option bid quote or the option ask quote?

I got SPX option prices from three different market data sources. In all of them, I can see bid and ask quotes. However, there is only one implied volatility. Does this implied volatility correspond ...
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What is the intuition behind a positive theta for European long puts?

I've googled extensively for an answer to this question. Very similar (if not identical) questions have popped up in this same website (example) but I never find the answers to be clear and/or precise....
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N-period state price deflators

Given that the non-dividend paying share is at $5. In each 6 future 6 month period its value can either rise by 25% or fall by 10%. The continuously compounded risk free rate is 5% p.a. Consider a ...
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Confusion Regarding Dynamically Delta Hedging a Short Option

To my understanding, market makers (mm) in the options market dynamically delta-hedge their portfolios by buying/shorting the underlying, thus eliminating directional risk and profiting from providing ...
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Data source for FX options

I have daily quotes for the new york and london fixings of fx options on EURUSD. I can choose between two sources: BGN and CMPN. Apparently these are based on slightly different methods of aggregating ...
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FX option quotation in interbank market

I am looking at the different ways in which FX options (say EUR/USD option) are quoted in interbank markets. Is it quoted using the option chain? I also saw a piece where it is said that it is quoted ...
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Is there an analogous strikeFromDelta implementation for 1st gen barrier options?

I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes ...
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What is the probability of touching point A first?

The probability of a stock touching a point A which is below the current spot price is 35%, and the probability of the stock touching a point B which is above the current spot price is 20%. How can I ...
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CMS cap has more vega exposure than CMS floor for same strike

When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that? I have a suspicion that it ...
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Unitise an options portfolio

Suppose I have a portfolio of European index options (long call, short put) and risk free assets (buy bank bills) to create a synthetic long index position. I wish to unitise this portfolio to ...
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