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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2answers
442 views

Caplet "in arrears" pricing formula

The forward Libor rate $L(t,t_1,t_2)$, with $0 \leq t \leq t_1$, must be a martingale under the T-forward measure associated with the zero coupon bond $P(t,t_2)$ that matures at time $t_2$. Pricing a ...
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1k views

Why is there greater demand for OTM and ITM options than for ATM options?

I´m currently writing a project on volatility trading and dynamics. The literature often states higher demand for OTM (out-of-the-money) and ITM (in-the-money) compared to ATM (at-the-money) options ...
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1answer
1k views

Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

I am trying to model $C(K)$, the price of the call $C$ as a function of strike $K$. Because this is tied to Prob ITM - and in fact the probability density function of that particular expiration (https:...
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4answers
352 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 time-to-...
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1answer
109 views

Show that $\frac{\partial c(t))}{\partial \sigma^2 }>0 \text{ if and only if } S(t)<Xe^{-r(r+\frac{1}{2} \sigma^2 )(T-t)}.$

Statement: if $c(t)$ is the price of the digital cash-or-nothing call option, then direct calculation (under Black-Scholes assumptions) shows that $$\frac{\partial c(t))}{\partial \sigma^2 }>0 ...
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5answers
12k views

What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?

Quoting Hull's book: When gamma is positive, theta tends to be negative. The portfolio declines in value if there is no change in S, but increases in value if there is a large positive or ...
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3answers
19k views

What is the relationship between Time-To-Expiry and Delta?

Is there any regular relationship between Delta and the Time-To-Expiry of an option? I have observed that options that expiry sooner are more sensitive to underlying movements (with equal strikes). ...
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2answers
4k 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: http://www.sharemarketschool.com/option-valuation-upper-and-lower-bounds-part-...
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1answer
3k 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: ...
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4answers
9k views

How to calculate the implied volatility using the binomial options pricing model

I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility. Please can you point me to paper or implementation (R, ...
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3k 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 ...
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1answer
775 views

"a straddle will be equal to two calls delta neutral or two puts delta neutral"?

I'm reading Nassim Taleb's book "Dynamic Hedging", on page 22 he says: Consequently, a straddle will be qual to two calls delta neutral or two puts delta neutral (of the same strike). Assume that ...
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1answer
5k views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
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4answers
14k views

Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options

The asset-or-nothing European option pays at t = T the value of the stock when at time T that value exceeds or is equal to the exercise price E, and nothing if the value of the stock is below E. So, ...
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2answers
717 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 ...
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1answer
508 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 ...
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2answers
2k 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 ...
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3answers
2k 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 ...
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1answer
287 views

Modeling liquidity effect on option prices

What are practically useful ways of modelling the effect of liquidity on options?
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1answer
378 views

How are the BKM risk-neutral moments derived?

I've been doing a lot of research on implied volatility skewness, and one of the most commonly cited papers I've come across is "Stock Return Characteristics, Skew Laws, and the Differential Pricing ...
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1answer
1k 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
2k 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 ...
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1answer
2k 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 ...
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1answer
1k views

Implied interest rate using put-call parity

In the process of asking this question, I acutally found the solution. I still let this post open if it can be interesting to someone else and have added a related question at the end. I want to ...
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1answer
4k views

Calculating dealer gamma imbalance/exposure for an options strip

Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
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137 views

Has a closed-form formula for the collateral choice option been found?

The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
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330 views

Libraries for calculating options strategy-based margin

Hopefully, this is an acceptable question in this forum, even if it isn't analytically focused. As part of an effort to analyse the effect of different option trade structures on a portfolio, I need ...
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1answer
229 views

Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
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3answers
9k views

Problems with local volatility models (vs stochastic volatility models)

Why is pricing with local volatility models are problem with exotics, mainly due to "the volatility surface is the market's current view of volatility and this will change in the future meaning the ...
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4answers
790 views

Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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4answers
654 views

Implied volatility of a complex options position

Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...
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3answers
527 views

Trading desk assumes zero percent discount rate?

All the swaption and option models I have encountered at my employer's trading desks have assumed a zero percent discount rate. I have proposed using the LIBOR curve, but management responded that &...
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3answers
1k 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}^{*}\...
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2answers
9k views

How do I calculate probability distribution of stock prices given option prices?

I'd like to calculate a probability distribution for prices given the option prices for that stock? Any ideas how to do this? My desire is to do this daily and then see how the price PD changes over ...
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524 views

How to price this option?

I was asked this question in an interview. There is an option as follows. It monitors the prices of two stocks A and B, and pays the difference in their prices at time $T$, if stock A has been higher ...
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2answers
1k views

Mathematical underpinnings of the square root of time rule

Often when I am reading about options pricing (and/or options greeks) the square root of time continually comes up. What the mathematical justification for why this keeps on turning up?
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2answers
653 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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3answers
8k views

Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...
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3answers
3k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
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1answer
959 views

Mean reversion time estimation

I am new to mean reversion trading, and I would like to get some good references about how to estimate the time it takes to a mean reverting process to cross its long term mean.
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2answers
415 views

Post Trade Analysis for Option MMs

What are the kind of post trade analysis (EOD analysis) that an options market making desk does? First few things that comes to my mind are slippages and breaking the pnl into various greeks. Any ...
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5answers
6k views

Writing an Options Strategy Backtester

I've been doing some digging, and this question has been asked many times in various forms over the years - Backtesting Options Strategies in R Are there any good tools for backtesting options ...
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2answers
2k views

Lower bound of ITM Calls when computing Implied Volatility

Assuming the Black Scholes model and pricing formula of a European call option. Then, if the call is ITM, i.e. if $ln(\frac{S}{K})>0$, the $d_1$-term will go towards infinity as $\sigma$ goes to ...
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2answers
1k views

Pair Trading Index Options

Suppose the trade is between Index Options of two Indices X and Y which are quite similar (but not exactly). So for the equivalent strikes, one can quote option on Index X and cover in Index Y. But ...
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1answer
3k 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: ...
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6answers
14k views

Option trading API other than Interactive Brokers

I'm looking for an options broker that provides an execution API. I'd like to ideally test on a papertrading version of it before connecting to a real execution engine. I know IB offers that, but they ...
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1answer
399 views

Options On Earthquakes

As a financial innovation, the options market is introducing Options contracts based on California Earthquakes. In your own words, discuss the following: True or False? “The sellers of Options on ...
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2answers
3k views

Dynamic Hedge of Quanto Options

Can anybody explain to me step-by-step how can I dynamically hedge and/or replicate a quanto option with the foreign underlying asset, the foreign cash account and the domestic cash account as ...
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1answer
239 views

Vol, Gamma, Vega -- essentially all the same?

When talking to traders I hear this sentence a lot I am a buyer/seller of X where X = {vol, gamma, vega} Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
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2answers
551 views

Implied volatility and nonconstant volatility

John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...

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