Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

2
votes
1answer
87 views

Why Can I not estimate a CVAR from Heston Model

I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected ...
1
vote
0answers
29 views

What are some beginner quantitative option trading strategies?

I'm new to quantitative trading, with good knowledge in finance and coding (mainly Python, Java, R, etc). I would like to know if there are any basic quantitative option trading strategies that can ...
3
votes
1answer
98 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 ...
0
votes
0answers
34 views

Solving for Implied Volatility Vega gets stuck at 0 (Python)

So my goal is to calculate option greeks with as few manual inputs as possible. I managed to get the IV for at the money options but then when I try further OTM strikes my results get completely ...
2
votes
2answers
73 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 ...
4
votes
1answer
77 views

Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?

The approximation is: $$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$ Background information from the first answer to this post: "Say that you have a portfolio of options with prices $P_j$. ...
6
votes
1answer
186 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 ...
2
votes
1answer
65 views

Derivatives Trading Jargon

Could you please help to understand trading jargon in this tweet. Thanks in advance. For non twitter users: Bookie pushing 5-delta (strike of 8) 2 month TRY puts. 0.6%
0
votes
1answer
138 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
34
votes
5answers
63k views

How can the implied volatility be calculated?

We all know if you back out of the B.S. option pricing model you can solve for what the option is "implying" about the underlyings volatility. Is there a simple, closed form, formula deriving Implied ...
1
vote
0answers
24 views

Where to Find Foreign Countries Index Option Data

OptionMetrics database contains option data for several US indexes (SP500, SP100...). But I don't see any option data for foreign indexes. Is there a place from which I could get/purchase the options ...
1
vote
0answers
45 views

Geometric Brownian Motion with Dividends

I am working on a problem and had a quick question. I understand that for Geometric Brownian Motion we use the formula: $$X_{t_n} = X_{t_{n-1}} + \mu X_{t_{n-1}} \Delta t + \sigma X_{t_{n-1}} \...
2
votes
0answers
45 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. ...
1
vote
1answer
424 views

Differences between Snowball, KIKO and TRF derivatives?

Can you explain what are some similarities and differences between snowball, KIKO (knock in knock out) and TRF (target redemption forward) derivatives?
5
votes
1answer
91 views

Pricing in the Heston Model

The dynamics of the Heston Model is \begin{align*} \frac{dS}{S} & = \lambda \sqrt{\nu} d W^S \\[0.5em] d \nu & = k (1- \nu )dt + \epsilon \sqrt{\nu} dW^\sigma \end{align*} where $\lambda$...
2
votes
1answer
64 views

Static hedge for up-and-out Digital Call

I am trying to come up with a static hedge for a Digital Call with strike K that knocks out when price > barrier H. I know it will involve non-knockout digital calls with strike K and strike H but I ...
1
vote
1answer
46 views

Asian Options Vs Bermudan Options

Which of these options are more popular in practice/used in industry? And where exactly are they used? Also, I have been searching for listed Asian and Bermudan options, for volume data etc, but have ...
1
vote
1answer
60 views

Looking for a Book

I hope everyone is well. While I was looking for derivations of Greeks I came across part of a book. Could you help me to find its name please ? Here is the link: http://centerforpbbefr.rutgers.edu/...
1
vote
0answers
28 views

Poisson parameter in Merton's Jump-Diffusion Model to price call option

I've been taught the following European call valuation formula under jump-diffusion model: \begin{equation} price = E[e^{-rT}max(S_T-K,0)] =\sum_{j = 0}^\infty e^{-rT}P_j(\lambda)E[max(S_T-K,0)|J=j] \...
4
votes
2answers
145 views

Factor model and trading strategy in options market

We all know that there are many factor models (CAPM, Fama-French 3...) and trading strategies (momentum trading...) in equity market. I wonder whether there are any analogous factor model and momentum ...
4
votes
0answers
61 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 &...
4
votes
1answer
44 views

Why is there no parameter for the estimated economic growth of a company in the option price model

Can someone explain me why the economic growth of a company is irrelevant in determining the option price. Especially for options with a long maturity e.g. 5 years it seems to me that for a high ...
1
vote
1answer
70 views

Black Scholes- Options and OIS

I have 2 questions. In the Black Scholes formula for currency options, where does forward premium come in? Volatility will be a historic parameter, so which component considers fwd premia. Typically,...
1
vote
1answer
44 views

How to understand firm option expiration cycle?

Here I am trying to understand the firm option expiration cycle: When I read Investopedia, it says: Most of stock options are on one of three expiration cycles, which consists of one month per ...
0
votes
0answers
8 views

How to plot the last values of a dataframe on boxplot? [migrated]

I have a 2*4 box plot, each contains 21 boxes. For each of them, I would like to plot the last value of each dataframe column. A closer look at one of them: ...
1
vote
1answer
152 views

Where can I get Currency options historical data?

where can I get historical data for currency options? For most part, google gives me links to binary options and other shady webpages.
0
votes
3answers
118 views

Options Delta Meaning of Term [closed]

not able to understand delta in options. Whilst I understand, it is how much the option moves when the underlying moves by 1 unit, I fail to understand, when someone books a currency option, why does ...
2
votes
1answer
73 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, ...
1
vote
0answers
37 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
1
vote
0answers
77 views

Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
6
votes
3answers
2k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
1
vote
1answer
78 views

Inherent volatility of selling longterm options and buying short term options

A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
6
votes
5answers
311 views

Heston Model Integration Oscillations

Is there a way to reduce oscillations for the numerical integration when evaluating the Heston model. I am pricing a series of 5000 options scattered over the Heston model parameter space and I find ...
1
vote
0answers
60 views

Pricing an exotic with barrier at discrete times

How would you price the following option on underlying $S$ without dividends? Time to maturity of option $\tau = 12$ months Option has a strike $K > 0$ and constant barrier $B > 0$. $t_0$ is ...
2
votes
0answers
85 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 ...
1
vote
1answer
50 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
4
votes
0answers
202 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 ...
29
votes
4answers
19k views

How to derive the implied probability distribution from B-S volatilities?

The general problem I have is visualization of the implied distribution of returns of a currency pair. I usually use QQplots for historical returns, so for example versus the normal distribution: ...
4
votes
3answers
484 views

use Monte Carlo or FDM to price Basket option

In the real practice, do we use Monte Carlo or finite difference method of PDE to price the ...
4
votes
2answers
171 views

Replicating the square of an option $C^2 (S,K,t,T)$

Given a vanilla options market, i.e. $C(S,K,t, T)$ for all strikes $K$, is it possible to replicate $C^2 (S,K,t,T)$? So I am looking for a self-financing portfolio which has a price equal to $C^2(S,K,...
1
vote
1answer
65 views

Can the value of a swaption at any time become more negative than the swaption premium?

I am interpolating swaption values as a function of parallel shifts in interest rate and have come across some peculiar shaped options among the data I have at hand. Here is an example of a simple ...
3
votes
2answers
594 views

C# - Using Black Scholes Newton returns NaN occasionally

First caveat: I'm a programmer doing this for a client, and my knowledge of options probably has holes in it. So be a little forgiving here. =) The Issue: When I run Black Scholes Newton against ...
3
votes
3answers
155 views

Risk-neutral density from spot prices?

I am currently working on a university project and I hope someone can help me out with a rather silly question :-) I want to analyse the change in the shape of risk-neutral density functions of spot ...
1
vote
0answers
20 views

Historical options data for FX/FI

I know that my question is quite large and that quite a lot of questions already deal with the options data. However most of questions deal with options on American equity markets. Could you ...
0
votes
1answer
42 views

Simulating stock prices with and without intermediate paths

So I am simulating stock prices with what I believe to be geometric Brownian motion using parameters from the usual Black-Scholes framework (Please correct me if I am wrong) with the following formula:...
1
vote
0answers
39 views

How to solve for K when setting the differential of a vega option with respect to K equal to 0?

The question is as follows: Let $v = S_0 \phi(d_1)\sqrt{T}$. Solve the following equation for $K$. $$ \frac{\partial v}{\partial K} = 0 $$ By finding $\frac{\partial v}{\partial d_1}$ and $\frac{\...
4
votes
1answer
132 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 ...
1
vote
1answer
97 views

Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
0
votes
1answer
40 views

Option pricing models relation between theoretical and actual price

I have trying to figure out the relationship between theoretical option price and actual market price spotted from market which is determined by supply and demand. I yet cannot understand how to ...
3
votes
0answers
76 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 ...