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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25
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8answers
2k views

Option pricing before Black-Scholes

According to the Wikipedia article, Contracts similar to options are believed to have been used since ancient times. In London, puts and "refusals" (calls) first became well-known trading ...
19
votes
6answers
6k views

What type of investor is willing to be short gamma?

As far as I understand, most investors are willing to buy options (puts and calls) in order to limit their exposure to the market in case it moves against them. This is due to the fact that they are ...
17
votes
5answers
11k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate ...
15
votes
3answers
2k views

Why hold options when you can dynamically replicate their payoff?

When holding vanilla options, you can cancel out, theoretically, all risk with dynamic (delta) hedging. Then you earn the "risk free rate of return". Why would you make such a portfolio when you can ...
15
votes
5answers
3k views

Skew arbitrage: How can you realize the skewness of the underlying?

It's not clear to me how to realize skewness. In other words, how do you implement skew arbitrage? There seems to be no well-known recipe like in volatility arbitrage. Volatility arbitrage (or ...
14
votes
2answers
506 views

Who has introduced the term 'vega' and why?

The sensitivity of the option value $V$ to volatility $\sigma$ (a.k.a. vega) is different from the other greeks. It is a derivative with respect to a parameter and not a variable. To quote from Paul ...
13
votes
7answers
6k views

What is the “delta” option quoting convention about?

At my work I often see option prices or vols quoted against deltas rather than against strikes. For example for March 2013 Zinc options I might see 5 quotes available for deltas as follows: ...
13
votes
6answers
1k views

Why are options trades supposed to be delta-neutral?

I'm reading Natenberg's book, and he says that all options trades should be delta neutral. I understand that this prevents small changes in the underlying price from changing the price of the option, ...
12
votes
6answers
939 views

Setting the r in put-call parity?

Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$. The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification. The variable $r$ is ...
12
votes
2answers
689 views

Can you fully hedge an option in the presence of counterparty risk?

The derivation of the Black-Scholes model assumes no counterparty risk. Does the presence of counterparty risk invalidate the argument behind the model? EDIT: The question is about options in ...
11
votes
3answers
3k views

Papers about backtesting option trading strategies

I am looking for all kinds of research concerning option trading strategies. With that I mean papers that publish results on different option trading strategies properly backtested with real-world ...
11
votes
3answers
3k views

Is there an all Java options-pricing library (preferably open source) besides jquantlib?

I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ...
11
votes
2answers
649 views

Can you replicate an option on an arbitrary basket of stocks?

Since a market index is nothing more than a basket of stocks, you can create your own index by putting together stocks of your choice. The only difference is that you can trade options on major ...
11
votes
2answers
3k 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: ...
11
votes
3answers
569 views

What benchmark/index to use for backtesting a portfolio of stock options?

What benchmark should I use for backtesting a model for when I should buy an option of a particular stock? For equities, one could say their portfolio outperformed the S&P 500. I would like to ...
10
votes
8answers
4k views

Why does implied volatility show an inverse relation with strike price when examining option chains?

When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ...
10
votes
3answers
1k views

When does delta hedging result in more risk?

There's a question in an interview book saying "when can hedging an options position make you take on more risk?" The answer provided is that "Hedging can increase your risk if you are forced to both ...
10
votes
5answers
626 views

Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock?

Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock? When a stock is too illiquid, there are some costs because of this ...
10
votes
1answer
245 views

How do you characterize dividends for equity options?

While many systems like to treat dividends as a continuous yield when pricing equity options, it works quite poorly for short-dated options. In the short run, deterministic dividends are clearly the ...
9
votes
5answers
5k views

What is the implied volatility skew?

I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that a clear standard definition is not unanimously in place among practitioners. So here is ...
9
votes
3answers
1k views

Why are there still manual market makers in options

Why are manual market makers still predominant in options markets? Why haven't algorithms replaced these market makers, as they have for liquid stocks for example?
9
votes
3answers
1k views

How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
9
votes
1answer
983 views

Is there a popular curve fitting formula of options skew vs strike price or vs Delta?

I was trying to build a options trading/optimization system. But it often gets more inaccurate as it scans through the far from ATM options because, you know, options skews. That is because I did ...
9
votes
2answers
315 views

When is it rational to exercise a bond option early?

Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
9
votes
1answer
335 views

Appropriate measure of Volatility for economic returns from an asset?

I am doing research on uncertainty analysis and risk assessment for oil field development. For doing economic forecast and valuation I use Real Options theory, which is almost similar to theory used ...
9
votes
3answers
892 views

Implementing a Fast Fourier Transform for Option Pricing

So, I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options. First ...
9
votes
1answer
1k views

Is QuantLib more trouble than it's worth?

I'm just starting to work with QuantLib and wonder if I'm going down a very wrong path. I'm working on a site that presents the visitor with a table of streamed real-time options data, including ...
9
votes
1answer
174 views

Breaking Transactions Down into Derivatives

We were talking about merger arb in a class I had last night, and when we got do deal construction it was mentioned that the different ways can be viewed as different options. For instance a fixed ...
9
votes
1answer
306 views

What drives changes in implied volatility on ETFs/ETNs?

I thought implied volatility, as well as the VIX, primarily increase due to increases in the underlying asset's volatility, as well as the options themselves being bid up because more people were ...
8
votes
2answers
2k views

When to use Monte Carlo simulation over analytical methods for options pricing?

I've been using Monte Carlo simulation (MC) for pricing vanilla options with non-lognormal underlyings returns. I'm tempted to start using MC as my primary option-valuating technique as I can get ...
8
votes
3answers
2k views

How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
8
votes
1answer
451 views

What are important model and assumption-free no-arbitrage conditions in options trading?

In the paper "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula" (Espen Gaarder Haug, Nassim Nicholas Taleb) a couple of model-free arbitrage conditions are mentioned which limits ...
8
votes
1answer
231 views

How should FX options be priced when a currency is artificially capped?

The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro. I would like to know if there ...
7
votes
4answers
1k views

Methods for pricing options

I'm looking at doing some research drawing comparisons between various methods of approaching option pricing. I'm aware of the Monte Carlo simulation for option pricing, Black-Scholes, and that ...
7
votes
4answers
1k views

Best way to store hourly/daily options data for research purposes

There are quite a few discussions here about storage, but I can't find quite what I'm looking for. I'm in need to design a database to store (mostly) option data (strikes, premiums bid / ask, etc.). ...
7
votes
4answers
674 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 ...
7
votes
4answers
2k views

How to obtain true probabilities from Black-Scholes?

How to obtain true probabilities from Black-Scholes option pricing equation? Suppose, that we know risk adjusted discount rate for the underlying asset (the drift term in the physical measure) and ...
7
votes
2answers
2k views

Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day? I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
7
votes
2answers
1k views

Is there a technique for using xts or zoo objects with options data (i.e., many entries per date) in R?

I am starting to work with options data from optionmetrics. I use data frames, but it seems like xts or zoo objects are the way to go for features and speed. I can't figure out the best work-around to ...
7
votes
3answers
508 views

How would one price a “credit event binary option”?

CBOE has introduced credit event binary options, kind of as a retail trader's CDS. These binary options are worth $1 if there is a credit event (ie, bankruptcy) before expiration, and $0 if there is ...
7
votes
2answers
1k views

What does the VIX formula measure and how does it work?

I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important. In semi-layman's terms, is the VIX ...
7
votes
2answers
237 views

What do we really mean by put-call ratio and how should it be expressed?

I need to calculate the put-call ratio for an American option. But I'm a complete naïf: I don't know how. I think I'd use the put open interest and the call open interest. I can imagine two ways to ...
7
votes
2answers
972 views

How to transform process to risk-neutral measure for Monte Carlo option pricing?

I am trying to price an option using the Monte Carlo method, and I have the price process simulations as an inputs. The underlying is a forward contract, so at all times the mean of the simulations is ...
7
votes
1answer
294 views

When pricing options, what precision should I work with?

I'm wondering if there's any point at all in double-precision calculations, or whether it's ok to just do everything in single-precision, seeing how the difference on non-Tesla GPUs for single and ...
7
votes
1answer
259 views

Inflation modelling

I am trying to price an option on the Spanish CPI. The option is a European call with a single observation date. However, I am fairly new to inflation modelling, so there are two areas in which I ...
7
votes
1answer
3k views

What is the best live options data API?

What is the best/cheapest service to get real-time (as real-time as you can get) on stock options? I'm looking for the fastest update on the ENTIRE market, with a few stocks prioritized, so I need ...
7
votes
1answer
166 views

How to handle coupon payments when pricing a bond with an embedded option?

I'm using a binomial tree to price a bond that has an embedded call or put option. On every node that has a coupon payment, do you include the coupon payment then max/min out the value, or do you ...
7
votes
1answer
1k views

How should I estimate the implied volatility skew term when calculating the skew-adjusted delta?

I'm trying to come up with the implied volatility skew adjusted delta for SPY options. I'm working with the following formula: Skew Adjusted Delta = Black Scholes Delta + Vega * Vol Skew Slope. I ...
7
votes
2answers
1k views

How to calculate the most realistic historical option prices with additional publicly available parameters

This is a follow up question of this one. My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes. The ...
7
votes
2answers
245 views

Extrapolating implied volatilities to small time

Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 ...