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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623 views

Papers and algorithms on bidding schemes for best order execution?

I'm building an automated option trading bot that executes common options multi-leg strategies (straddles, spreads) and I want to learn the best way to execute my orders. As you know, the bid-ask ...
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3answers
315 views

Given markets usually fall fast and rise slowly, are there trading mechanisms to take advantage of this?

Per a previous question on this topic -- markets generally fall fast and rise slowly: what options strategies or other strategies can one use to take advantage of this common occurrence?
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4answers
4k 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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5answers
619 views

In Black-Scholes, why is $\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t)}$?

Namely, I dont understand why the mean is $(\mu - \frac{1}{2}\sigma^2)\triangle t$ and not just $\mu \triangle t$. I am aware that it is supposed to represent a lognormal distribution, but I guess I'm ...
4
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1answer
150 views

Link between Vega and Gamma

"The vega is the integral of the gamma profits ( ie expected gamma rebalancing P/L) over the duration of the option at one volatility minus the same integral at a different volatility...Mathematically,...
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2answers
200 views

Is there a better way to price options than with historical volatility?

I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...
4
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2answers
480 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
399 views

How to quickly sketch a second order greek profile for a vanilla position?

Assume that you are given an arbitrary payoff profile for European vanilla position (e.g. butterfly). How to make a back of the envelope sketch of a second order greek profile for it (i.e. plot ...
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1answer
72 views

Why buy/sell a forward starting option?

More precisely, in equity markets, why would one prefer to buy a forward starting option over a vanilla option ? What about the selling side ?
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1answer
152 views

How to use the Black-Scholes formula with LIBOR rates?

I want to price an FX option using the Black-Scholes model, but I don't know the risk free rate, nor the volatility. I only know the LIBOR rates, the strike, and that the expiration day is 87 days ...
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2answers
118 views

simple, intuitive barrier option derivation

Is there a simple integral that gives barrier option prices without having to deal with messy, hard PDEs and change of variables I understand there is a reflection principle such that the simulation ...
4
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2answers
744 views

Black Scholes vs Binomial Model

I'm trying to confirm my understanding of the 2 models. It is my understanding that the black-scholes is a special case of a binomial model with infinite steps. Does this mean that if I were to start ...
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1answer
193 views

Hedging with actual volatility: problem understanding the math behind the result

From this paper. page 3 We get that the total profit at expiration is the difference in value between the price of the option with actual volatility and the one with implied volatility. I have tried ...
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2answers
95 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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votes
1answer
717 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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1answer
179 views

questions on VAR manipulation

The book of Financial Risk forecasting by Danielsson gives the following example about VAR manipulation. I have two questions: 1) If $0> VAR_1 > VAR_0$ , why the following figure plots it as $-...
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1answer
307 views

Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
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votes
2answers
990 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
748 views

Science behind options pricing into Earnings event

I am wondering about studies regarding the uncanny options pricing into public company's earnings reports. The phenomenon being that the price of a straddle before earnings costs near exactly the ...
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2answers
56 views

How to replicate a correlation swap using only vanilla options and underlying

Assume I have two assets A and B that are positively correlated most of the time. I'm trading a strategy based on this correlation. Is there a way to protect myself in the event that the correlation ...
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3answers
63 views

Constant Maturity IV

I want to analyze IV skew under various market conditions but its hard given various expirations. Would it make sense to create a constant maturity IV that say is 60 DTE? Has anyone done this and what ...
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1answer
95 views

Call options and portfolio of the same options worth less?

A portfolio of long positions in call options with the same maturity and strikes on different assets is worth more than a call option on a portfolio of the same assets with the same weight; i.e. $$\...
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1answer
199 views

VXV vs. VIX futures: arbitrage opportunities?

At a first glance, VXV and VIX futures should not be compared at all: VXV is an underlying index, whilst VIX futures are derivatives written on a different underlying index, that is, VIX. As instance,...
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2answers
275 views

How to trade leveraged ETFs

Leveraged ETFs (LETFs) are known to lose value over time due to the "volatility decay" effect. What're the most common strategies for trading LETFs to take advantage of this volatility effect? Also, ...
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1answer
177 views

What does the “-E” mean at the end of a CBOE options symbol?

Below is are some option quotes taken directly from the CBOE website. I am wondering what the -E, -4, -8, -A, -B, -I, -J etc..that are at the end of the options ...
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2answers
174 views

Time-independent local volatility

Suppose somebody provides us with a surface of European call prices $C(\tau,K)$ where $\tau$ stands for time-to-maturity and $K$ for the strike. By Dupire's results, there is a unique local volatility ...
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2answers
2k views

Drawbacks of Black-Scholes option pricing model

Will highly appreciate if anybody can provide logical financial proof why the Black-Scholes option pricing model overestimates the value for long-term options as described in this paper "Warren ...
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3answers
333 views

self-consistent parametric form for equity implied volatility

I recall reading a paper, but can't remember where I found it. In short, there was a parametric form for volatility smile/skew that fit both index and single stock vol slices and had intuitive ...
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1answer
384 views

What are good conditions to roll a leap further out in time?

If you're hedging with a back month / leap option, what are good underlying / market conditions to move this option out even further in time? For simplicity, let's say you own a call with 6 months ...
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1answer
542 views

Standard Deviations out the money where options will respond to underlying asset price changes

Is there an understood way of determining how far out the money an option can be, before it starts/stops responding to the underlying asset price changes? I usually look at the greeks, gamma, delta, ...
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1answer
422 views

European turbo warrants

Totally new to the world of quant finance, so perhaps this is an odd question... Does there exist an American equivalent to the German style "knock out zertifkate"? (The name might be slightly wrong....
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2answers
468 views

Hedgefund-like behavior for covered call selling account?

I make money selling covered calls on FX spot options, and some of my friends want to buy in to this without having to trade their own accounts. One method is for each of them to get an account, ...
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votes
2answers
231 views

How to derive Black's formula for the valuation of an option on a future?

I've got a question about 1976 Black Model and Bachelier model. I know that a geometric brownian motion in the P measure $dS_{t}=\mu S_{t}dt+\sigma S_{t} dW_{t}^{P}$ for a stock price $S_{t}$ leads (...
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1answer
135 views

Understanding skew of SPX - Why does IV of OTM puts increase with strike?

I've been trying to understand the skew I see when looking at the skew of SPX. Here is a snapshot today from thinkorswim. I understand why IV increases for ITM puts -- namely because there is a ...
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1answer
65 views

When are ES E-mini future options issued?

Since options lose 2/3 of their time value in the second half of their lifespan, it makes sense to be aware of when an option was issued. What are ways of figuring out when ES futures options have ...
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1answer
168 views

Literature on Empirical Option Pricing

When I started combing through the literature I was astonished about how little the option pricing models are tested against market data and benchmarks are limited. The main barrier is of course ...
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1answer
596 views

Option based portfolio insurance in practice

My question is about option based portfolio insurance in practice. Some insurance companies offer products where there is a mutual fund (equity and bonds) and a guarantee attached. This guarantee is ...
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1answer
232 views

How to synthesize a futures spread option?

Is it possible to synthesize a futures spread option using only the options on the spread's underlyings? If so, how? If not, is there another way? As an example, please show me how to synthesize ...
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votes
1answer
190 views

Creating a doubling and halving position

I want to create a position that either multiplies with $1+u$ (outcome $U$) or $1-d$ (outcome $D$). The probability of $U$ is denoted by $P(U) = \pi$. The initial value of the position is $V_0$. Given ...
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2answers
618 views

Does put-call parity hold for a compound option with underlying American option?

Say there is an American put option that expires $N$ months from today. A call-on-put (CoP) option provides the owner the right to buy the American put option in exactly $M < N$ months (but no ...
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1answer
81 views

What are the answers to these questions on card deck and option pricing?

here are 3 questions I have some trouble dealing with. Your help will be greatly appreciated! 1 - We have a deck card: 26 red, 26 black. we play a game: you draw a card from the deck without putting ...
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1answer
78 views

Butterfly spread model price

Consider a butterfly spread with strikes $K_1, K_2, K_3$. My professor wrote the model price, $V$, was equal to the following: $$V = exp(-rT) * P(K_1<S_T<K_3) * (1/2) \Delta K$$ where $\Delta K ...
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1answer
106 views

Vendor data aggregation for Options on Futures

Have anyone managed to automate data consolidation between Reuters and Bloomberg for Options on Futures? Are there any common attributes that these vendors share in this particular asset class that ...
4
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1answer
97 views

Forced to exercise gap options

I was reading a textbook and came across some surprising stuff in the section about gap options. Let $X$ be a payoff function such that $X=\Big\{\matrix{0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...
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1answer
148 views

Options on Volatility Control Index

I have two question. Does an option on volatility control index exist? If I google it, it seems like there is such an option, but I can't find the option on any of exchanges. So this is my first ...
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1answer
230 views

US options market/microstruture research

Can someone point out where to find up to date market/microstruture research in the options market?
4
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1answer
148 views

At-the-money Call Spread approximation

In a trading manual I got during a course, the value of the ATM Call-Spread is approximated by $CS_{ATM}=\frac{1}{2}StrD+(F-m)\times\Delta CS$ The lecturer skipped the part where he derived this ...
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2answers
2k views

Equity option portfolio greeks with underlying

I'm curious about how to construct the five basic greeks for an equity option portfolio when there are shares of the underlying in the portfolio. For example, a portfolio of 100 call options and 100 ...
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1answer
202 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
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2answers
1k views

Options pricing exercise - American call option on a futures contract

I am confused by a particular exercise I am doing right now, I am hopeful that someone can walk me through as to how to solve it. I further hope the question is not considered too basic for this forum....