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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How to extrapolate implied volatility for out of the money options?

Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ...
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3answers
3k views

What really drives option implied volatility?

A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
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2answers
3k 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 ...
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2answers
2k views

Implied Volatility from American options (binomial)

I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock). I believe it is ...
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3answers
962 views

On the interface between Quant finance and actuarial-science/insurance-math

Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model. People going into quant finane or striving to become a quant on ...
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2answers
2k views

Beta vs. Implied Volatility statistical arbitrage using options

Let two underlyings, $S_{1}$ and $S_{2}$, are correlated and $\beta$ is the slope of their returns linear regression, that is, it says how much $S_{1}$ co-variates with $S_{2}$ variance. For ...
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4answers
829 views

Replicating portfolio and risk-neutral pricing for interest rate options

For equity options, the pricing of options depends on the existence of a replicating portfolio, so you can price the option as the constituents of that replicating portfolio. However, I am not seeing ...
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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 ...
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229 views

What is more appropriate: the EMA of the option price or the EMA of the underlying?

I'm progressing, all too slowly, on a site that aims to show real-time numbers for options that are listed on the CBOE. Most of the instantaneous numbers are all set. Now I'm going to pay attention to ...
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1answer
375 views

How do you calculate the implied liquidity of an option?

How does one calculate the implied liquidity of a specific option contract given a set of vanilla puts and calls with various strikes and maturities on a single underlying?
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2answers
288 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 ...
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1answer
330 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 ...
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1answer
385 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 ...
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2answers
2k 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 ...
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2answers
1k views

Can one use options on Treasury futures to hedge a portfolio?

Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step ...
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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 ...
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295 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 ...
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266 views

Derivation of Stochastic Vol PDE

A couple questions regarding stochastic vol PDE derivation. Following Gatheral, a general stochastic vol model is given by \begin{align*} dS(t) & = \mu(t) S(t) dt + \sqrt{v(t)}S(t) dW_1, \\ dv(t) ...
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4answers
667 views

Why does it take so many lines of code to price even the simplest of options with QuantLib

I have been looking at QuantLib I am trying to figure out why I need to write so much boilerplate code even when pricing the "simplest" of European Options using the analytical Black-Scholes formula ...
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2answers
3k views

using quantlib function in my c++ program

I want to include the QuantLib function for option greeks calculations in my own C++ code. My question is: can I just include those functions? I don't want to use the rest of their stuff. I obviously ...
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6answers
14k views

How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)

I am looking for one line formula ideally in Excel to calculate stock move probability based on option implied volatility and time to expiration? I have already found a few complex samples which took ...
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1answer
437 views

Arbitrage opportunity interview question

I have seen this interview question mentioned in a couple of places: There are three call options on the market, with the same expiry and with strikes 10, 20, and 30. Suppose the call option with ...
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2answers
361 views

What changes to put-call parity are necessary when evaluating american options on non-dividend paying assets?

If an underlying doesn't pay dividends (for our purpose defined as any distribution to the underlying's holder) directly or indirectly (e.g. options on futures) how does put-call parity change from ...
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2answers
196 views

How to price an option allowing to change a call into a put?

A recruiter asked me this question: Suppose you have the following contract: a call option with maturity T = 2 years the possibility to change this call into a put at t = 1 year What is the price ...
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2answers
4k views

Why FX Vanilla Options are quoted in volatility

I've been curious why vanilla options are quoted (and traded) in terms of volatility. Considering that every financial institution has its own options pricing model, volatility as an input would cause ...
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1answer
215 views

Prove or disprove “If at least 10% of an option's value is time value, it has a delta less than 90”

"If at least 10% of an option's value is time value (ie. time value >= 0.1*call price), it has a delta less than 90". In practice and after doing many tests with an option pricing calculator, this ...
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1answer
1k views

Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
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2answers
183 views

how we can derive $PIDE$ of double exponential Jump-diffusion model (we know as kou model)?

I'm working in double exponential Jump-diffusion model (we know as kou model) with following form , under the physical probability measure $P$: \begin{equation} ‎\frac{dS(t)}{S(t-)}=\mu‎‏ ‎dt+\sigma ...
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2answers
214 views

What's the point of discounting in risk-neutral pricing?

Let $\phi$ be a self-financing strategy that replicates a time $T$ option payoff $X$ on stock $S$. By definition of a trading strategy, $\phi$ is previsible. Finally, let $V_t$ be the time $t$ value ...
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1answer
3k views

Implied dividend estimation

I am looking at two different ways of estimating the expected / implied dividends from market data. 1. Dividend futures I know that this asset class is not very liquid and might not be ...
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4answers
3k views

How does an option's time value depend on moneyness?

How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
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1answer
699 views

How to calculate equivalent futures position?

Let's say I have the following two positions: Buy ATM SPX call, expires in 1 month Sell ATM SPX put, expires in 1 month This creates a synthetic futures position. How do I calculate how many ...
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6k views

How to replicate a digital call option

Call Option S=100 K=100 Payoff=1 (option is not available) How can i replicate this (payoff) with calls and puts with strike prices with multiples of 5$ Thanks for help
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3answers
401 views

Parameters for pricing option on EDF

Ladies and Gents, Im writing a quick routine to calculate implied vols for options on EUR$ futures with Bloomberg data. My question concerns the part where I have all my inputs and am ready to pass ...
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0answers
198 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: ...
6
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1answer
243 views

Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...
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6answers
797 views

Why the expected return rate of a stock has nothing to do with its option price?

OK, I admit that this is a frequently asked question. But I couldn't find a satisfying answer after I read the explanations of books, went through the derivations of B-S formula, and searched answers ...
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2answers
195 views

The Upper Bound of an American Put Option

I have just read the following paragraph (in bold) and have a question on the upper bound of an american put option: ...
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4answers
297 views

Shorting an option every day vs shorting only at maturity

Suppose we have 2 strategies : strategy A : every $N$ days, we short a call option with a time-to-maturity of $N$ days; strategy B : every day, we short $\frac{1}{N}$ of a call option with a ...
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1answer
909 views

What are the main flaws behind Ross Recovery Theorem?

Stephen Ross’ new paper claims that it is possible to separate risk aversions and historical probabilities if the Stochastic Discount Factor is transition independent using Perron-Frobenius Theorem. ...
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2answers
293 views

Does it make sense to use upward and downward volatility in option pricing?

Historically stocks have a higher likelihood to increase in price than to fall in price. As such would it make sense to split a stocks volatility measurement into upward and downward components? For ...
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1answer
109 views

Valuing a warrant on a warrant

How would you go about valuing a European warrant that entitles you to a) 1 share of a company and 2) 1 warrant on that same company?
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2answers
482 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 ...
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1answer
258 views

Modeling liquidity effect on option prices

What are practically useful ways of modelling the effect of liquidity on options?
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2answers
843 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
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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
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1answer
374 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 ...
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1answer
582 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 ...
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1answer
705 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 ...
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1answer
702 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 ...