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.

313 questions with no upvoted or accepted answers
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204 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 ...
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506 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 ...
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207 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, ...
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47 views

Leverage of various option types

Does the standard European option calculation of leverage, Embedded Leverage = Delta times (Underlying price/Option price) change across the various option ...
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42 views

Replicating portfolio with stock, bond and call option

I am trying to interpret: I am having trouble interpreting the replicating strategy: Context: $\phi$ is a generic payoff function, 0 < S < $\infty$, assumed throughout to be twice ...
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22 views

Data sources for historical ICE settlement option prices, volume & open interest

I am looking for long history for historical settlement option prices, volume & open interest at ICE Europe (specifically fixed income). This seems to be more challenge than I could imagine. ICE ...
2
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20 views

Implying a required rate of return on an option from the required rate of return on the underlying

Is it possible to imply a required rate of return on an option from a required rate of return on the underlying? For example, given a known cost of equity, can you calculate the required rate of ...
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32 views

CVA for options

I am trying to do a simple unilateral CVA for call and put options. I found this discretised formula online: $$ CVA = \sum_{i=1}^m \frac{EE(t_{i-1})DF(t_{i-1}) + EE(t_i)DF(t_i)}{2} \left( PD(t_i) - PD(...
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52 views

Delta Hedging Example

I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...
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37 views

Stratified sampling in asian options

I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
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42 views

what is the state of the art method for hedging barrier options?

I want to create my own Barrier options for some security, I want to trade. I did some literature review, and found a static replication method, and many dynamic replication methods. I want to know ...
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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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47 views

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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40 views

How to calculate the multiple integrals where the integral domain is based on the sum of normal distribution random variables?

The integral is shown below: And how to use python to calculate pi (better if we don't need to code for each pi)?
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32 views

How to calculate the risk neutral probability of the underlying price always exceeding the lower barrier K during a given time?

I'm trying to price the autocallable structured products by a probability approach proposed in the following paper: Modeling autocallable structured products, by Geng Deng, Joshua Mallett, Craig ...
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58 views

Banks' use of written interest rate options

I study US commercial banks data. I look at the notional amounts of their different OTC interest rate derivatives for the recent years. When I look at non-dealer banks (i.e. end-users), I find that ...
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158 views

Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads

I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
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71 views

How to determine expected returns of an options portfolio?

Lets say I have a delta neutral portfolio, iron condors on spy for example. I'm short a call credit spread and a put credit credit spread of equal widths. I would like to determine the expected ...
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55 views

Risk-Neutral Pricing with Regime Switching

As the title suggests, I am currently trying to implement a dual regime-switching options pricing model. In its simplest form, I am fitting a risk-neutral GARCH(1,1) to a crash and normal regime. ...
2
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2answers
116 views

American Option Exercise

Suppose I am a market maker in American options. At end of day I have positions in various options but my portfolio is overall hedged. Now, after the market close, someone decides to exercise an ITM ...
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212 views

Fitting Gatheral's SVI model

I was considering using Gatheral's formula for fitting option skew. In the specific (commodity) market that I am concerned with, the underlying is ca. at 50, and typically 5 integer strikes left and ...
2
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417 views

Using QuantLib Python to value FX options using stochastic volatility

I would like to use QuantLib (and in particular the python wrapper) to value FX option using the Heston model. Thanks to http://gouthamanbalaraman.com and all of the articles therein : in particular ...
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1answer
114 views

Where can I get some Inflation Option example quotes (year-on-year and zero-coupon)

I am writing an academic paper on calibration of inflation vanilla options. I need to generate examples for the paper. Is there anywhere I can get example data for the Inflation year-on-year options, ...
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126 views

Bimodal option pricing based on P.D.F

is there any literature on option pricing given the pdf of the underlying asset - e.g. i am interested in seeing how prices for a range of strikes ought to compare based on, say, a simple normal ...
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208 views

Binomial Model Implementation Trouble - American and European options come out equal

I'm Trying to implement the binomial option price model in python and get reasonable performance by using memoization. I checked the output against a black and scholes model and for European options ...
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35 views

About buying and selling a cumulative parisian options

I ask my question here because I want to know more about the cumulative Parisian options introduced by M. Chesney, Mr. Jeanblanc-Picué and Mr. Yor in 1997, then developed by Hugonnier in 1999 and F. ...
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168 views

Arbitrage from ATM option trading?

So I was testing out a collar options strategy (long put, short call, and long shares of the underlying stock) in a backtest for a school finance project, and the profits & losses are given by the ...
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182 views

Discrete time option gamma hedging

1) An option $V$ under the Black-Scholes model is perfectly hedged when it is delta hedged continuously with the underlying $S$. When the hedging time is discrete, the delta $\Delta$ needs to take ...
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55 views

Do you receive premium from selling VXTY futures?

I am having some difficulty understanding VXTY futures and how they are priced. The contract specs say it is priced off of OZN options (10yr UST futures options). I understand there is a premium ...
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106 views

Control Variate Barrier Basket Option

I need to improve the speed of convergence of PRNG Monte Carlo. I'm opening a new thread for that purpose and I have question / need confirmation about the algorithm. I'm pricing options with Heston, ...
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170 views

Extrapolating implied dividend yield

I have liquid option quotes for 1, 2, 3 and 4y expiries. I was able to imply the continuous dividend yield for all of those. How would you extrapolate such implied yield to 5 and 6y expiries?
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152 views

Exotic derivatives - Replication

I would like to replicate the payoff Max(0, Min(S1, K) - S2) with a combination of the following derivatives: -> option on S1, strike of our choice -> option on (S1-S2), strike of our choice -> A ...
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50 views

Multiple max/min forward start option

I want to calculate the price at $t$ for such payoff at $T$ $$\max(S_T,S_{T_0},C),$$ $$\max\left(S_T,\min(S_{T_0}, C)\right),$$ $$S_T -\min(S_{T_0}, C),$$ $$t<T_0<T.$$ Is there any way or ...
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63 views

Options pricing, dividend taxation

I have a question. When pricing, do an equity option, dividend has to be taken into account of course, however since there's a taxation on the dividend does the dividend input has to be cut by the ...
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201 views

American put option in binomial model - arbitrage opportunity?

I'm sorry this must be an elementary question. I spent a good deal of time searching through webs including this site for the problem but I got none. Here's the problem: Say we have a binomial tree ...
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2k views

Black-76 Model for Swaption Price and Greeks

I'm in the early stages of developing a swaption pricing model. Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
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288 views

Implied Vol skew VS Local Vol skew (as presented by Derman 1995)

I am reading Derman's article/notes regarding local volatilty: http://www.emanuelderman.com/writing/entry/the-local-volatility-surface. I am examining the graph on page 13. The Implied volatility (...
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102 views

Theta from Black-Scholes PDE - is it possible to use implied volatility?

There is a need to derive theta $\theta$ of an option out of standard Black-Scholes PDE. In usual notation ($P$ - price of an option, $S$ - underlying spot): $\theta=r_dP−Sr_d\delta−\frac{1}{2}\...
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119 views

American options — doing better than Black's approximation when $r = 0$

I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid ...
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112 views

Barrier Option with Time-Dependent Rebate

Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed? ...
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293 views

Pricing of multi strike rainbow options

I am looking at the pricing of a two asset multi strike option in the Black Scholes framework but I am struggling with coming up with a pricing formula. The payoff of the option at maturity is \...
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161 views

Option pricing formula for deep in-the/out-of money options?

I am learning option pricing and trying to calculate the call and put price using the Black-Scholes Formula. I have calculated the historical volatility to be 0.232. The formula is gives value close ...
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78 views

Practical precision for Options Pricing

When pricing options, especially in the theoretical literature getting high precision, say up to 8 decimal places is always a competitive goal. Though realistically in a practical setting is such ...
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44 views

Looking for material on volatility forecasting with a focus on market/news events

I'm hoping someone can direct me towards any books/papers that approach volatility forecasting from the perspective of market specific events (fed meetings, USDA reports, OPEC announcements etc). From ...
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147 views

Option delta under Black mode vs SABR

Under what scenarios would the Deltas for Options on Bond Futures differ the most between Black vs SABR models ?
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81 views

'Market price' based Delta vs 'Model Price' based Delta for Bond Future Options?

My understanding of Delta is the change in the Option's price relative to the change in the underlying asset's price. In the case of Treasury Future Options (ie those on CME), one intuitive way to ...
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487 views

GARCH Option Pricing Model (Duan 1995)

I am trying to replicate Duan's results from his 1995 Paper, "The GARCH Option Pricing Model". I have written this code in Python myself, and using his parameters I consistently seem to obtain results ...
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1k views

Pricing of European Power Call Option via Black-Scholes formula: reasoning?

I want to price a European Power Call option (without dividend yield) with payoff $\max\{S_T^2-X, 0\}$, where $T$ is the maturity and $X$ the strike. Let $(S_t)_{t\ge 0}$ be the price process of an ...
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660 views

Delta hedging vs Strangle

Long volatility delta hedging and strangle are common long volatility strategies. We can make strangle delta neutral(in $) by buying more puts than calls(if an absolute value of put delta is less than ...
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351 views

Trading strategies for increased realized volatility

Suppose once every 2-3 weeks I have a way to select a few equities that are likely to exhibit higher realized volatility in the future month (relative to the past month). Historically, the average ...