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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303 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
315 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
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1answer
196 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
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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
259 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 ...
6
votes
2answers
507 views

What are the major models for energy derivatives, particularly electricity derivatives?

Aside from Black-Scholes with crazy skews, what major models are used for energy derivatives? I'm thinking particularly of electricity derivatives, but I'm also interested in natural gas and other ...
6
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2answers
2k views

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 ...
6
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3answers
2k 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 ...
6
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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 ...
6
votes
1answer
349 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?
6
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1answer
196 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 ...
6
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2answers
169 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 ...
6
votes
1answer
99 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?
6
votes
2answers
216 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 ...
6
votes
3answers
229 views

What is the fair price of this option?

Without having to use Black-Scholes, how do I price this option using a basic no-arbitrage argument? Question Assume zero interest rate and a stock with current price at \$$1$ that pays no dividend. ...
6
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1answer
2k 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 ...
6
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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 ...
6
votes
4answers
2k 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 ...
6
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1answer
589 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 ...
6
votes
1answer
455 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
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1answer
538 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
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1answer
571 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
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3answers
378 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 ...
6
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0answers
423 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 ...
6
votes
4answers
560 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 ...
5
votes
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 ...
5
votes
2answers
294 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 ...
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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
327 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 ...
5
votes
1answer
1k 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
594 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
1answer
418 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
1answer
147 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
430 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. ...
5
votes
1answer
587 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
2answers
1k 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
360 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 ...
5
votes
1answer
229 views

Modeling liquidity effect on option prices

What are practically useful ways of modelling the effect of liquidity on options?
5
votes
1answer
335 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 ...
5
votes
1answer
176 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: ...
5
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2answers
311 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
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0answers
110 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
5
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0answers
504 views

option chain data visualization, sunburst

I think option chains are not represented in the best way. With more and more options products coming out and trading on the various exchanges, I see vendors struggling to keep up with a good way to ...
4
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5answers
918 views

Do binary options make any sense?

Reading from "www.nadex.com" - the copy reads "Binaries are similar to traditional options but with one key difference: their final settlement value will be 0 or 100. This means your maximum risk and ...
4
votes
5answers
8k 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 ...
4
votes
6answers
3k 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
4answers
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 ...
4
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2answers
425 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 ...
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2answers
801 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 ...