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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1answer
2k views

What is the formula for beta weighted delta and gamma?

I am trying to calculate the beta weighted delta and gamma for a portfolio of options of different underlying stocks, but I can't seem to find the correct formula. Can someone point me to it or a ...
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0answers
39 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 ...
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42 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 ...
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2answers
207 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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47 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 ...
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1answer
179 views

How to get the probability of exercise call option in Black-Scholes model?

From Black-Scholes model, I'm trying to prove: $p(S_t>K) = N(d_2)$ No luck yet! Can anyone suggest a reference showing that how to obtain this equation? All I get is: $S_t = S_0e^{ (\mu-0.5 \...
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1answer
202 views

Intraday option price data European stocks and indices

I am looking for intraday option price data for stocks and indices listed on European markets (SX5E, SMI, DAX, etc). Ideally, I would like to get files as clean as those provided by ivolatility for US ...
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1answer
1k views

Backtesting on historical option data

I have downloaded some daily historical option data for a timespan of 10 years and want to perform trading backtests with them. Data are European index options, on ODAX. My question is about realistic ...
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0answers
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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80 views

Greeks Intraday Characteristics and PnL of options

I am modeling intraday and short term options on Futures.Think Monday, wednesday, friday contracts on these tickers: ES, NQ, CL, ZN, ZF, NG. I am wondering about documentation for Intraday greek ...
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1answer
153 views

Binomial Tree Option Pricing Model. Lets talk dividends and futures

I am writing an option pricing model for production use. Its not for arb or anything so it doesn't need to be 100% as accurate as possible. Just good enough for "what happens to my book if we jump 10 ...
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1answer
158 views

Dependency of an option price on time till expiry

I am trying to seek satisfaction when it comes to understanding why the price of an option is dependent on the time until expiry. I have read that the longer till expiration, the more time available ...
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2answers
105 views

Naked options selling [closed]

I sold the naked put. The price of underlying went down and broke the support. The situation changed technically from bullish to bearish. The price of underlying is still quite far above the option ...
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3answers
234 views

Who trades exchange options in practice (Margrabe's formula)?

I'm currently studying the pricing of the exchange option. https://en.wikipedia.org/wiki/Margrabe%27s_formula While I can appreciate the theory, who actually buys these options in practice? Are ...
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1answer
98 views

How to derive and interpret the duration of a call option?

I read here that CFA students are taught that $$ D_{C} = \frac{\Delta_{C} D_{B} B}{C} $$ Where $D$ is the duration, $\Delta_{C}$ is the first derivative of the options price with regards to the ...
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1answer
54 views

European put price when stock price is 0 before maturity

According this answer, https://quant.stackexchange.com/a/39298/29108, the European put price (with maturity $T$) at time $t$ for a stock whose current price is $0$ should be the strike $K$ discounted ...
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0answers
145 views

Is SABR being used in practice for Equity options

Just to be clear: By "in practice" I mean what the banks and other financial companies do. Do financial companies use SABR for pricing equity options? Consider a stock with price $t$ being: $S_t$. ...
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1answer
102 views

Equity repo close to money market rates?

I've noticed that the repo rate (here I mean the effective financing rate of the forward position in stock) implied from synthetic forwards is almost the same as money market benchmark (XXXibor 3M) ...
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0answers
44 views

Calculating Risk of Portfolio of Futures/Future Options [closed]

all. I am looking into calculating margin on futures mixed with futures options. Say ES is trading at 2700 currently, I long 100 ES, 600k (Margin/risk). Then i buy 100 2680 puts. so Points Diff (...
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23 views

Does a shift in prices effect Margin on Futures and their options?

In regards to ES im wondering If theres a scenerio intraday (price shock) that will effect the amount of margin im carrying. Besides PnL Kind of a dumb question, as I guess its just a function of ...
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2answers
269 views

How is volatility different from variance?

I always thought volatility was just variance ^ (1/2). Now I'm reading this book and it's saying that the two are different concepts. Excerpts include: Partly due to its use in Black-Scholes, ...
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1answer
115 views

Expected payoff at future time

Let $a$, $b$, $c$, and $e$ be constants, $W_1$ and $W_2$ be Brownian motions with correlation $\rho$, and $f(t)$ and $g(t)$ be deterministic functions of time. Let $X$ satisfy $$d(X(t))=(aX(t)+ef(t)g(...
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1answer
3k views

Early exercise of American options

I know this question is considered basic and has been asked millions of times, but I have done my research and there are some points that I just can't understand. For an American call, many ...
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1answer
56 views

Black Scholes modified boundary conditions

Compute the price of the payoff $(2\log(S(T))-K)^+$. Before I do any algebra, I want to make sure I understand. To solve this problem, I need to solve the Black Scholes PDE with boundary condition $C(...
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1answer
232 views

Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)

There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example: Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
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0answers
77 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 ...
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2answers
89 views

Pricing options with 0 or negative underlying values

I am trying to calculate the value of an option whose underlying is the calendar spread between two months for a commodity (front month Brent vs 2nd month), usually known as a calendar spread option. ...
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0answers
33 views

Volatiliy in a at-the-time call option [duplicate]

I understand that the vega of the Black-Scholes equation is a positive function, which means the value of the option is an INCREASING function of the volatility, since vega is the derivative of the ...
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1answer
85 views

Barrier Option from binomial tree

What is the smallest information structure that is required for using the binomial tree to calculate the price of a barrier (up-and-in) option? My gut feeling is any node below the node that reaches ...
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2answers
122 views

Greeks and options hedging

Why is it that theta is sometimes taken as the proxy for gamma of the underlying asset in options hedging?
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0answers
79 views

Term structure of the ATM implied volatility of short term weekly options

It's an empirical fact that the implied volatility of short term weekly options are significantly higher than options that expire in a few weeks, and the volatility of the near term options get even ...
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0answers
62 views

replicate option by dynamic hedging

I've just started working for a company with a decent commodity exposure. They manage this by as they call it dynamically hedging it. Basically when they start the hedging they identify a market ...
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0answers
73 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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0answers
117 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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2answers
723 views

What is the formula for Intraday and overnight volatility?

I'm a noob trying to calculate IntraDay and Overnight Volatility. For Intraday volatility we can get the annualization factor with the following: Length (hours, Open to Close): 6.5 Time frames per ...
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1answer
90 views

European put options

Why is it that for European Puts on Non-Dividend-Paying Stocks, the lower-bound for price is $$p=Ke^{-rT}-S_0?$$
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4answers
2k views

From Fourier Transforms to Option Values

I am trying to understand how Fourier transforms & Characteristics functions can be used to calculate option values. However, I am having difficulty following the process that is used in several ...
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2answers
265 views

What is the Brownian motion in the model for the return of a stock price trying to capture?

I have read that in the derivation of the Black-Scholes PDE, we assume that the return of a stock $S$ is given by $$\frac{dS}{S}=\mu dt+\sigma dB$$ where $\mu$ is the average growth of $S$, $\sigma$ ...
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0answers
124 views

Black Scholes Replicating Portfolio Riskfree Asset

Im having a question about this standard derivation of the Black-Scholes formula: http://www.soarcorp.com/research/BS_hedging_portfolio.pdf The paper states $$C=\Delta S+B$$ and finally $\Delta = ...
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1answer
106 views

Why Quantlib Option NPV does not change when repricing?

Trying to learn Quantlib with Python, please have a look at below code: ...
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1answer
65 views

Filter options used in the construction of implied volatility surface

Currently trying to model the IV Surface using the APPL options, to compare how different models of the underlying move the IV Surface. However, after getting the data, I've seen that some option ...
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0answers
191 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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2answers
204 views

Justification of Levered ETFs?

I have done some basic research on levered ETFs and cant understand them completely How do you justify the existence of Levered ETFs when margin accounts are available? E.g. If I want 3X SPY returns, ...
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2answers
134 views

Seagull Spread payoffs

I'm looking at different option strategies and the ways that their payoffs differ (and therefore how they can differently be used). I'm looking at the long seagull (buy a call spread and sell a put), ...
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2answers
68 views

Synthetic equity index futures calendar spread using options

I understand it is possible to synthetic a future using long call and short put ATM options which has the same expiry as the futures. Can we do the following to synthetic a future calendar spread? $...
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1answer
64 views

Iron condor with positive vega

I am backtesting this Iron Condor before earnings. In the position summary Vega (Mid Quote) is -3.04\$ but in the chart below (IV vs Profit $) it's clearly shown that a decrease in volatility will ...
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1answer
208 views

Probability ITM formula for options

Given a stock of price price and annual volatility annual_volatility, and given an option with strike price ...
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1answer
172 views

Delta hedging/Gamma PnL

Suppose I am long USDIDR straddle with my start of the day delta being USD10m long IDR and USDIDR gamma being $5m. There is a 1% intra-day IDR strengthening, so my delta becomes roughly long IDR 15m....
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13answers
17k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
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3answers
2k views

Writing an Options Strategy Backtester

I've been doing some digging, and this question has been asked many times in various forms over the years - Backtesting Options Strategies in R Are there any good tools for backtesting options ...