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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
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2answers
21 views

What is “Lambda” in Heston's original paper on stochastic volatility models?

In his paper (link), he has the equations: b1 = k + ƛ - (ρ * σ) b2 = k + ƛ k is the rate of mean reversion, ρ is the correlation between the two Wiener processes, σ is vol of vol, what is ƛ? ...
1
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0answers
43 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 ...
0
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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
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%
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 $P_j$. ...
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
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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
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0answers
46 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
61 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
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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] \...
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 ...
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 ...
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
2answers
146 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
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,...
0
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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
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 ...
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 $\lambda$...
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 ...
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 ...
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 ...
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 ...
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 ...
1
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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 ...
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 ...
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
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,...
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 ...
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 ...
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 ...
2
votes
1answer
70 views

Pricing an fx option in the same currency

Let imagine we have an option from EUR to USD priced in EUR, therefore the payoff for a call is: $$\frac{(S - K)^{+}}{S} = K (1/K - 1/S)^{+}$$ This is basically the payoff of a price of a put on 1/S ...
0
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0answers
35 views

How to hedge PLN account on Interactive Brokers

I know that you can't have PLN account on IB, the PLN input is exchanged into USD, GBP etc. currency. However I would like to hedge the other currency exposure against PLN, or at least find out how to ...
3
votes
0answers
47 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 ...
0
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0answers
91 views

Exotic option arbitrage

Suppose an exotic European option has a sub hedging (price being lower than the target) portfolio of vanilla European options all with the same expiry as the exotic option. The sub hedging portfolio ...
2
votes
1answer
56 views

is relating bounds to relation between time to maturity and european put option price correct?

J.C. Hull derives the following relation $$Ke^{-rT} - S \le p \le Ke^{-rT}$$ where $p$ is european put option price, $K$ is strike price, $S$ is stock spot price,$r$ rate of interest and $T$ ...
0
votes
1answer
150 views

What is market standard model in equity, FX and interest rates exotics?

Is there any industry consensus about the model to use for pricing exotics in equity, FX and interest rates? I assume that for vanilla options they all use Black model, but how about exotics? Also, ...
-1
votes
1answer
126 views

Equity Derivatives Question [closed]

I'm preparing to take a test on equity derivatives and have met with some difficulty, so I need some help on the following question: Please analyze the following share purchase plan. Assume client ...
1
vote
1answer
87 views

Barrier Option Valuation

Good day, A reverse knock-out barrier call option expires worthless if the asset price ever goes above a given barrier level. Calculate the value of this barrier option struck at $K = 3$ with ...
1
vote
1answer
80 views

Hedging strategy for American Option

Good day, I was asked to devise a hedging strategy for an American Option given the following claims. Note, $r=0$ and the underlying stock pays a dividend of $1$ at time $t=1.5$ \begin{...
1
vote
1answer
105 views

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

Problem: Deep in the money options contracts will be assigned at expiration date. Higher Volume ratio of deep in the money contracts at expiration calls or puts leads to day after expiration date we ...
2
votes
0answers
121 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 ...
1
vote
2answers
75 views

Option value with different spot prices [closed]

I found this post online which is plotting different results for option value and greeks depending on spot price. Why would someone want to do calculate the value of the option with different spot ...
1
vote
0answers
32 views

Correct beta weighted delta options formula?

Is this the correct formula for beta weighted delta: http://www.nishatrades.com/blog/beta-weighted-delta I've seen this What is the formula for beta weighted delta and gamma? but they seem to be ...
1
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0answers
38 views

Is there a way to pull SPX index option open interest daily data?

Currently I just use Bloomberg API in Excel for preliminary data analysis and manipulation, and I have one function call that gives me the ticker and IV today ...
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, ...
0
votes
2answers
145 views

What is the second derivative with respect to price of a put option? [closed]

What is the reasoning/meaning behind the second derivative of a put option
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0answers
42 views

What is the true “value” process of American derivatives?

Consider a continuous-time market where LOOP (law of one price) holds. The first fundamental theorem of asset pricing states explicitly that in the absence of arbitrage, the risk-neutral measure ...