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.

286 questions with no upvoted or accepted answers
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1k views

option chain data visualization, sunburst

I think option chains are not represented in the best way. With more and more options products coming out and trading on the various exchanges, I see vendors struggling to keep up with a good way to ...
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357 views

What is the most convenient data structure for backtesting a model of futures options prices?

I have an empirical model for the dynamics of futures prices in a particular market that I have implemented using a long series of the front five contracts. (I account for the roll in my model.) I ...
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208 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
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239 views

Libraries for calculating options strategy-based margin

Hopefully, this is an acceptable question in this forum, even if it isn't analytically focused. As part of an effort to analyse the effect of different option trade structures on a portfolio, I need ...
6
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0answers
248 views

implied volatility and strike price

Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$. How is it possible to show that the ...
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198 views

Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$...
6
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215 views

How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
5
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1answer
382 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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234 views

pricing option with two stocks

Let $\left(S_t^{(1)}\right)_{t\ge0}$ and $\left(S_t^{(2)}\right)_{t\ge0}$ be the price processes of two stocks with dynamics $$ \begin{align} & dS_t^{(1)}=\sigma_{11}S_t^{(1)}dW_t^{(1)} \...
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127 views

Risk neutral measure in exponential levy model

Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ...
4
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50 views

Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
4
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75 views

Is there an arbitrage free option model that treats volatility as a deterministic function of strike?

I am trying to get a good understanding of the different models out there, and thus be able to study hedging errors, and strengths and weaknesses. My understanding of the Local Volatility model in ...
4
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118 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
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78 views

Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
4
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1answer
122 views

Which securities have expirations more often than monthly?

I'd like to explore buying low-cost calls close to the money, so I'm looking for low time values in options premiums. This happens near options expiration. Unfortunately, most options expire on the ...
4
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0answers
79 views

Structured Energy Option Pricing

Let's say I have an option with the following terms. This is for an energy product (ie natural gas) The contract will last for 6 months The payoff is the difference between the first of month index ...
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223 views

Higher Order Greeks

In studying options pricing a while back, I had learned of the higher order sensitivities of of Speed and Color. Speed was the rate at which the gamma changes with the underlying. Color is a ...
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454 views

How to estimate option implied skewness and kurtosis in R

Suppose that i have data that for each day i have more than one option, either put or call. I.E. I have more than 20 put options and 20 call options for each specific day. What is the way to estimate ...
4
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151 views

Match different option high frequency databases

I downloaded the “E-mini S&P 500 (Dollar) Options for 1/10/11” Top-of-Book (BBO) data. If you are interested you may download the data from the following link (approx. 80MB zipped and 1GB unzipped)...
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83 views

Are there academic papers on the 'term structure' of adverse selection for futures and options?

By term structure I mean a non-stationarity in the pattern of intraday adverse selection as a given instruments approaches its expiry. Note that I am interested in the adverse selection on the ...
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94 views

Forecasting amount of slippage in executing option spreads

Is there a good quantitative model to estimate how much slippage is required to execute a particular option spread trade? For example, let's say you want to execute an Iron Condor. Given X, Y, Z ...
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203 views

How to price an option with two volatilities?

Imagine you have two volatilities, the second which is "activated" when the stock crosses a barrier called $p_b$. The present price is $p_1$. ($p_b>p_1$). This can be used to price options after a ...
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231 views

What is the longest number of consecutive days that options implied volatility has stayed “extremely high” for any particular underlying?

Curious as to whether or not there is any sort of all time record. Any index, future, or stock will do. Volatility must be well above the average 1 year volatility for all periods.
4
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1answer
189 views

Correlation sensitivity of Rainbow options

I read from various sources (eg. Exotic Options and Hybrids, M. Bouzoubaa) that the correlation sensitivity of Rainbow options (say a call price on a basket made of 50% of the best stock, 20% of the ...
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34 views

Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
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41 views

Rainbow option pricing formula under *Bachelier* model

Let's consider a call on min option on two underlying arithmetic Browniation motions $V_t$ and $H_t$ (no drift). Let $P_t$ denotes the price process of the option, $r$ the riskfree rate, $\tau$ the ...
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45 views

Why not discount the dividend in the european put lower bound condition?

According to the european put lower bound condition: $ p \geq max(D + K \cdot e^{-r(t_2-t_0)} - S_0, 0)$ where $t_0$ is now and $t_2$ is maturity. Say $t_1$ is the dividend release time where $t_0&...
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91 views

Uniqueness of the Hedging strategy

I am currently reading the book "Nonlinear Option Pricing" by Julien Guyon. In the book they defined an attainable payoff $F_T$ as a $\mathcal{F}_T$ measurable random variable for which there exists ...
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51 views

How to Compute the payoff of Var Swaps, which I have replicated

I used Derman(1999) method, to calculate the fixed Kvar for Variance Swaps using actual option price data. The first Pic Shows the outcome. (ignore the 0s). Now the profit and loss of short var swaps ...
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200 views

Bachelier Pricing Formula for Interest Rate Binary Options

Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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110 views

How to interpret CDF($d_1$)/PDF($d_1$) from BS model ?

In my research on put options, I come across the ratio: $\frac{(1-\mathcal{N}(d_1))}{\mathcal{N'}(d_1)}$ where $d_1=\frac{\log(S/X)+(r+\sigma^2/2)t}{\sigma \sqrt{t}}$ and $\mathcal{N}(.)$ is the ...
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117 views

Usages of variance swap

I’m interested in variance swap. Considered from its feature, variance swap is used for betting the (historical) volatility of underlying asset. If we use it for hedge tool of Vega or Volga, does it ...
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75 views

American CRR implied vols

Given I have all other parameters lined up with the market (borrow rate, dividends...), if I imply volatility using CRR tree from american call and put with the same strike and expiry, will I always ...
3
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309 views

Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal

In the link below, in the text it states the following equations: Delta-hedged straddle P&L = Volatility Risk-premium ×| Straddle Vega | and Delta-hedged risk-reversal P&L: ...
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64 views

Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
3
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158 views

Parametric VaR of a portfolio of a stock and an option on that stock

I understand how to calculate the parametric VaR of a stock and an option separately. But I don't understand how one can calculate the VaR of a portfolio of a stock and an option on that stock using ...
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154 views

Early Exercise Options and Coin Flipping

This problem was presented in an interview, and I know I got it roughly correct. But I am still not entirely understanding the early exercise component of it: Say I am advertising a game where I ...
3
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0answers
607 views

Rationale behind volatility dispersion (or correlation) trading

When looking at the explanation of CBOE S&P 500 Implied Correlation Indices available here, it is written that such indices: [...] "may be used to provide trading signals for a strategy known as ...
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0answers
109 views

Pricing Options on Fixed Income ETFs

The market for trading options on fixed income ETFs like HYG has become increasingly prominent in the past couple years, but I've been unable to find any discussion related to the pricing methodology ...
3
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63 views

Delta hedging and PF-value

Imagine buying a call option and shorting the delta. After some time $dt$, the stock price changes, and so does the delta and the call option value. We re-adjust our hedge using this new delta. ...
3
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0answers
73 views

ODE Solution in Carr's Randomized American Put

In Carr's 1998 paper Randomization and the American Put, he sets up the following ODE for the value of an American put with expiration given by the first jump time of a Poisson process with rate $\...
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1k views

Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
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0answers
482 views

How to price Swaptions with short rate models?

I have specified a (Lognormal) short-rate model (non-affine) under the Risk-Neutral measure $Q$ as a shifted exponential vasicek: $ r(t) = e^{y(t)} + \phi(t)\\ \text{with} \quad dy(t) = \kappa(\...
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133 views

Example of optimal delta hedging in G. Barles, H.M. Soner option pricing paper

There is a paper Option pricing with transaction costs and a nonlinear black-scholes equation by Guy Barles and Halil Mete Soner. And there is a section about optimal (delta) hedging, which I do not ...
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0answers
396 views

Modeling market sentiment and pricing options by volume, open interest

Are there any empirically-proven methods/formulas for weighting IV surfaces, pricing a discount/premium in an option, and/or adjusting any of the 1st- or 2nd-order Greeks for the magnitude (volume or ...
3
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0answers
142 views

Pre- Versus post-2008 Crisis Rates Modeling

Modeling for interest rate derivatives (such as bermudan swaptions) is said to have undergone significant changes since the crisis. Prior to the crisis, counterparty default risk was often ignored, ...
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139 views

Estimating risk aversion (power or exponential utility) from options prices

I came across this literature and it seems like there are a number of ways people do this. You can do it for an option on any underlying as long as you can create the risk-neutral p.d.f. If you agree ...
3
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0answers
201 views

Pre-Trade Slippage Costs For Option Spread Execution

Is there a quant model that can help estimate how much slippage one would have to give up in order to get an "option spread" (vertical, butterflies, etc.) order executed? What factors should one look ...
3
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0answers
493 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
3
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0answers
200 views

How to find the upper bound of a digital option given some market data?

Given the price of a call equals to 5 with Strike 100, please find the upper bound (sup) of the digital option with strike 105. I am not sure about the solution, but I write the condition like this, ...