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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6
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2answers
513 views

How can one determine approximately what percentage of options trades are buyer-initiated vs. seller-initiated?

How can one determine approximately what percentage of options trades are buyer-initiated vs. seller-initiated? What measures of order flow are available specifically for options, preferably for ...
6
votes
1answer
259 views

Modeling liquidity effect on option prices

What are practically useful ways of modelling the effect of liquidity on options?
6
votes
2answers
862 views

Heuristics for calculating theoretical probabilities of being ITM at time T for listed options

I'm looking for a heuristic way to calculate the probabilities of being in the money at expiry for non-defined risk options combinations (listed options). I use delta as a proxy for this probability ...
6
votes
2answers
1k views

How to derive appropriate volatility for a binary option (with strike/term) from market data?

I am valuing a binary FX option (european) with a defined strike and term (2Y). I'm using a closed form solution based on Black-Scholes framework. How can I derive the appropriate volatility to use ...
6
votes
1answer
380 views

What are VIX back-month futures based on?

The VIX calculation is a weighted average of prices for front-month out-the-money options on the S&P index. So for VIX futures, this makes sense for the front month vix futures (being based on a ...
6
votes
1answer
600 views

How sensitive are vertical spreads to changes in implied volatility?

How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money? I'm thinking for 1 point spreads this would be very small / neutral ...
6
votes
1answer
724 views

Need historical prices of EUREX American and European style options

I am trying to get the historical price data on selected American and European style options at EUREX. I am not familiar with their system. Does any one know whether they have something like yahoo ...
6
votes
1answer
745 views

What is the best method to compute project volatility in Real Option Valuation?

There are few methods like Copeland-Antikarov, Herath-Park, Cobb-Charnes etc. to compute project volatility, however these methods compute upward biased volatility. What is the best method I could ...
6
votes
3answers
161 views

Creating Options Database

I am trying to create a database which will hold information for various stock options and will need to be updated daily. The idea is to use this database to keep track of changes in the open interest ...
6
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1answer
770 views

Can options volume have an impact on the price of the underlying asset?

Can options volume affect the underlying asset price indirectly? I know that options buying/selling does not directly affect the price of the underlying asset (rather, the asset price contributes most ...
6
votes
1answer
180 views

Quantifying Hedging Error Due To Expiration Day Range?

Let's say I have two call option liabilities that I want to statically hedge with a single call option. Liabilities: Liab_Call_1: Strike: 100 Notional: 1000 DaysToExpiration: 20 Liab_Call_2: ...
6
votes
0answers
200 views

How should option prices differ when using the Heston versus the Black-Scholes model?

I am running Monte Carlo simulations for a European Call using Heston Model and I am trying to compare them with prices calculated using Black-Scholes formula. I am not quite sure if the prices I get ...
5
votes
5answers
14k views

Why do some people claim the delta of an ATM call option is 0.5?

I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5. I have seen many books quoting delta of ATM call ...
5
votes
5answers
2k views

How to price a calendar spread option?

How do you price calendar spread options, that is, options on the same underlying and the same strike but different times to maturity? Clarification: I'm interested in the pricing of a a CSO (...
5
votes
2answers
448 views

Algorithmical replication of a profit and loss function using different options

I often see questions like "Given this payoff graph (example below), construct a portfolio that replicates it." I want to know if there is an efficient method/algorithm to find the individual pieces ...
5
votes
3answers
112 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 ...
5
votes
2answers
487 views

What does put-call parity imply about option premiums?

We know that $$C-P = PV(F_{0,T}-K)$$ When we create a synthetic forward, we buy call and sell a put at the same strike price $K$. When we buy the call why do we assume the premium is positive? When ...
5
votes
3answers
139 views

Binary Option in B-S model - technical question

I want to price Binary Option in Black-Scholes model. The payoff is of the form $f(S_{T})=I_{\{S_{T}-K>0\}}$. If we assume that $t=0$ this is easy, because then we have $C_{0}=\mathbb{E}^{*}\...
5
votes
2answers
1k views

Constructing an approximation of the S&P 500 volatility smile with publicly available data

Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW. Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
5
votes
2answers
753 views

Why are options called what they are called?

This may be a very obvious question, but can someone tell me where and when the names call and put originated? And similarly, where do the terms American and European option come from? Aside from the ...
5
votes
1answer
4k views

Call option arbitrage opportunity

I am having trouble wrapping my head around some text provided to us by our lecturer (unfortunately he is currently unavailable). If we let $c$ be the price of a European call option, $S_0$ the ...
5
votes
1answer
2k views

How would I value a perpetual bond with an embedded option?

I am trying to work out how to value the following transactions. It should be straight forward, since it breaks down into a series of well known instruments, yet I am not sure how to evaluate it: ...
5
votes
1answer
724 views

How to apply quasi-Monte Carlo to path-dependent options?

Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
5
votes
2answers
180 views

How to calculate Implied Volatility for out-of-the-money options?

I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ...
5
votes
1answer
261 views

Closed form solution of PDE of Option Price

Let $V=V(S_t,t)$ be the option price and \begin{align} V_t+\mu\,S\,V_S+\frac{1}{2}\sigma^2\,S^2\,V_{SS}=0\\ V(S_T,T)=\ln (S_T)^{2}. \end{align} My question: How can I obtain a closed form solution of ...
5
votes
1answer
812 views

QuantLib: Black / BSM processes and pricing via volatility surface. Different results?

I start this question with a couple of C++ functions that will be useful to show some results. So start your Visual Studio C++ Express or Ceemple or whatever you want and copy & paste this: ...
5
votes
2answers
105 views

Calculating probability of Yuan's slump from options market

http://www.bloomberg.com/news/articles/2016-01-06/if-options-traders-are-right-the-yuan-s-slump-is-far-from-over Contract prices indicate a 79 percent probability that the currency will weaken ...
5
votes
4answers
240 views

European Call Option Delta Upper Bound

For a pure equity process (with interest rate, dividend, etc., being zero) not necessarily the geometric Brownian motion, is the delta of a European call option always no higher than $1$? I am NOT ...
5
votes
1answer
323 views

How to use a change of numeraire to price this option?

I recently asked this question regarding how to price an option with payoff: $$\text{Payoff}_T = (A_TR_T - A_T \lambda)^+ $$ Let's assume for generality that $A_t$ and $R_t$ are GMB's: $$dA_t = \...
5
votes
1answer
242 views

How to approximate the time to mean reversion for implied volatility

Given an option and its implied volatility, and also the mean value of the implied volatility over the last 30 days, if we find that the current IV is significantly (> 1 std dev.) away from the mean, ...
5
votes
1answer
138 views

What is the mechanism of Asian option?

I have no problem with the mathematical definition of an Asian option. For example, assume the strike price is $K$, the expiration date is $T$, the underlying asset has price $S(t)$, and the payoff is ...
5
votes
1answer
757 views

Modified bisection formula for deriving implied volatility for a dividend paying american option

I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield). On page 171 of Haug The ...
5
votes
1answer
63 views

Where to find E-mini S&P options price data or chart?

ES futures price data is easy to find, e.g. on Yahoo finance or with a free NinjaTrader demo account. I'm looking for the same for options on that futures contract. The best I could find is the ...
5
votes
2answers
137 views

Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
5
votes
2answers
668 views

good R package for vectorized option pricing

I am using for now the package fOptions but it doesn't allow for vectorized computation of black76 prices and delta. Which package can be used to do that? As noted ...
5
votes
2answers
234 views

Covariance structure of call option surface

Assume the observed call option prices $C(K_i,T_i)$ for $i = 1,\dots,N$ are disturbed by some unknown measurement noise $\epsilon$. What would an appropriate covariance structure be for $\epsilon$? ...
5
votes
1answer
152 views

Which volatility to use to price options on futures contract?

I have some questions regarding pricing futures options and I just want to be sure that my thoughts are correct. I am trying to price options on futures for american & european style. In the ...
5
votes
1answer
247 views

Difference between a warrant and an option?

What is the difference between a warrant and an option on a stock? Apparently both represent the same right to receive a share of stock at the strike.
5
votes
2answers
2k views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
5
votes
2answers
2k views

VIX = Vega of S&P500 options?

ok, so let assume I can predict the daily change in the VIX itself (in points) every day. what would be the best way to play this with OPTIONS? well, obviously VIX options, but if I can look at the ...
5
votes
2answers
119 views

Solution for american perpetual put

I have been attempting an exercise in which I have to determine the value of an american perpetual put, $P$ in terms of the asset value $S$. The solution to the exercise says: When $S>S_f$ (the ...
5
votes
1answer
383 views

what's the relationship between forecasted stock volatility and implied volatility?(option)

what's the relationship between forecasted stock volatility and implied volatility? I know that implied volatility is the volatility calculated by BS formula, is there any relationship between implied ...
5
votes
2answers
330 views

Pricing options under restricted domain

How would I price an option when the underlying security is unable to trade above a certain price? I assumed this would be as simple as restricting the limits of integration of the PDF to B (the ...
5
votes
1answer
357 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 ...
5
votes
0answers
170 views

Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$...
5
votes
0answers
181 views

How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
4
votes
2answers
646 views

Why an option has sometimes and implied volatility greater than 100%?

Sometimes, in an option chain, the implied volatility of an option is greater than 100% . How is this possible? I mean, it is possible for 100$ stock to increase more than 100%, but not decrease more ...
4
votes
3answers
6k views

Does implied vol vary for calls vs puts?

Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
4
votes
6answers
5k views

Call vs. Put Option

I have two interrelated questions that have been bothering me for some time. I have read all the stuff online and it still doesn't make sense to me: Let us assume: 0% interest rate (both hedge ...
4
votes
2answers
1k views

Why doesn't a simulated delta hedging process go to zero?

I put together a simple simulation of delta hedging a set of options with an underlying and it seems that the fluctuations of the price still seem to affect the final outcome. The reason, I understand ...