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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.

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Naked options selling

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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42 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
58 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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25 views

Intuition behind pricing derivatives irrespective of the drift of their underlying stock [duplicate]

I have been trying to understand this concept for a while now and I have read the solutions to questions on the same topic, but I feel all the answers miss the ‘intuition’ behind the idea and I was ...
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33 views

Calculating Risk of Portfolio of Futures/Future Options

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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20 views

Future options and the dynamics [closed]

Elaborate to me in depth how future options work and how to price them? How can I get to profit from? or use them for hedging purposes?
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1answer
97 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
44 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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0answers
69 views

Calculating min/max price range using volatility

I'm trying to reconcile two methods of forecasting price ranges with say 95% confidence over a 50 day period given the annual365 IV say 19.1% = 1% daily volatility take the daily standard deviation ...
1
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1answer
60 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 ...
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1answer
42 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
62 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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0answers
32 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 ...
4
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1answer
69 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
86 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
41 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 ...
8
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1answer
180 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
40 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 ...
1
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1answer
110 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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0answers
43 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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2answers
100 views

What is the economic reason for the equality in value of an American call and European call?

In a previous question this question came up. In my mind, if I'm holding an option at time t, then there are possible future price paths where at t+k the option will be ITM but at T the option will ...
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0answers
41 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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0answers
51 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 = ...
2
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1answer
84 views

European put options

Why is it that for European Puts on Non-Dividend-Paying Stocks, the lower-bound for price is $$p=Ke^{-rT}-S_0?$$
3
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1answer
44 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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2answers
171 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
55 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
197 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
38 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), ...
1
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1answer
34 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
55 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
85 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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2answers
169 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, ...
4
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1answer
106 views

Splitting theta from vol carry

What is the best way to splitting theta and vol carry on say a long calendar trade? Basically trying to split the "good" carry component of a trade from the "bad" carry (theta) which could be earned ...
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0answers
28 views

Data request: Option prices for a liquid index/stock

Currently doing a course project on option pricing as a part of my undergraduate studies. However I cannot find a free dataset $D=[d_1,d_2,...,d_N]$, which would represent a time-serie of daily option ...
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0answers
24 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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0answers
37 views

Valuing stock employee compensation securities

This may be a simple question but I wonder if Im oversimplifying it. I'm trying to decide how to value different Stock Employee compensations and in particular a Stock Appreciation Rights (SAR) Reward....
3
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3answers
168 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
44 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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3answers
79 views

How to compute gamma for at-the-money regular calls and puts when they approach expiration to avoid explosion of portfolio's gamma?

When and at-the-money regular call or put approaches expiration, gamma tends to infinity. However, for practical purposes, there is only a finite change in delta. The problem is that if any of the ...
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1answer
72 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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35 views

What is the use of undiscounted Futures/Option Prices

Reading the great book of Gatheral on Vol Surfaces (link) I can't help but notice that throughout he uses undiscounted option prices (though he obviously never assumed rates to be zero). See e.g. ...
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2answers
54 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? $...
3
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0answers
105 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 ...
4
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3answers
199 views

arbitrage free volatility surface

Why is calendar spread arbitrage equivalent to $\partial_t \omega(k,t) \geq 0, \forall k \in \Bbb{R}$ where $\omega(k,t) = \sigma^2(k,t) t$ and $\sigma(k,t)$ represents the Black-Scholes implied ...
4
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1answer
102 views

Heston model computations

In the Heston model the dynamics of a single-asset $S$ are given by: $dS_t = rS_tdt+S_t \sqrt{V_t}dW^S$ where $W^s$ is a brownian-motion $W^S$ and the square root variance process $V$ is given by ...
3
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1answer
92 views

Basic questions on options, implied volatility and SPY

I am a bit confused about the impact of implied volatility on options, SPY options especially. I know that option's price decays with time and that is positively correlated with implied volatility but ...
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1answer
115 views

Why are implied volatility and the volatility required for an option to be profitable two different things?

SPY currently trades at $278, a put option expiring in 7 days against SPY, at this strike price, quotes \$2.40. This means one person (the option buyer) is betting SPY will quote below $280.40 (278 + ...
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2answers
37 views

CME Eurodollar Option qoute

How are the premiums/prices for eurodollar options qouted. Does the option price for one underlying future contract equals the qoute*100. As I see the option price 9750 CALL expiring in Sept 2019 as ...