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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2
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2answers
180 views

How to synchronize put and call option-data?

I recently retrieved a large amount of European option data, for call and put prices, from OptionMetrics. Doing so for the same time period I get a file consisting of 62558 rows of call prices & ...
5
votes
3answers
7k views

Implied Volatility Calculation

We all know if you back out of the BS option pricing model you can derive and solve what the options is "implying" as its volatility. However, what is the formula used to derive IV (can anyone direct ...
4
votes
1answer
1k views

Call option arbitrage opportunity

I am having trouble wrapping my head around some text provided to us by our lecturer (unfortunately he is currently unavailable). If we let $c$ be the price of a European call option, $S_0$ the ...
0
votes
2answers
156 views

monthly contract volume required for penny increments?

Have the exchanges disclosed their criteria? Does anyone have a best guess based upon observations of volume (however you wish to define it)? Please no qualitative answers.
2
votes
1answer
339 views

Calculating the probability of a price change using an options pricing formula

I don't know if I'm doing this right and I'd greatly appreciate help. I'm trying to use an option pricing formula to backout the likelihood of the Euro dropping below $1.27, even for a minute, at any ...
0
votes
2answers
156 views

changes in open interest vs changes in underlying volume

Has a relationship been noted? Mostly, I'd like to know if the open interest increases on an underlying, does the underlying usually see increased trading? My guess would be "yes" since MMs can ...
3
votes
3answers
1k views

Does implied vol vary for calls vs puts?

Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
4
votes
1answer
182 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 ...
3
votes
2answers
116 views

Endogeniety of Black-Scholes

I know this is a naïve question but how does the BS formula have a closed form solution? It seems from what I am reading Price impacts delta, price influences volatility which in turn influeces delta ...
2
votes
2answers
989 views

Theta's effect for OTM options

How does $\Theta$ change for deep out-of-the money options? Looking at the below graph, it seems the time decay is highest for ATM options and increases rapidly as we approach maturity of the option. ...
3
votes
2answers
2k 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 ...
5
votes
0answers
394 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 ...
2
votes
1answer
246 views

Can a long put trade be profitable through Vega even if the underlying moves upwards?

Generally speaking, I know when implied vol increases, option prices increase for calls. However, does the same occur for puts? If I am expecting implied volatility to increase for an option on an ...
3
votes
1answer
222 views

how to define liquidity in equity, index, and etf options

i've heard several ways to put a metric on liquidity of options.. obviously liquidity isn't a constant.. things like the Bid/Asks spread, liquidity of the underlying.. Trying to find a way to ...
2
votes
1answer
139 views

OTC Equity Options' Dynamics

This only applies to options that do not have marketable equivalents since margin can be marked to them. I've never been able to find this on my goog. How is margin typically calculated for OTC ...
4
votes
2answers
609 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 ...
2
votes
1answer
619 views

How to calculate implied volatility and greeks in Bull Put Spread option strategy?

Ok, obviously I am buying lower strike put and selling higher strike put. What is the recommended volatility and greeks to consider in my trade? Volatility: Average volatility between both legs? ...
4
votes
5answers
5k 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 ...
4
votes
2answers
233 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 ...
1
vote
2answers
461 views

Delta of a Down and Out Call

I came across some graphs depicting the delta of a down-and-out call. They show that, if the risk free rate of return is 0, the delta is constant at 1. However, if the rate of return is for example ...
2
votes
2answers
779 views

How to calculate Vomma of Black Scholes model

This source (PDF) gives the closed-form for vomma (or volga, i.e. the second derivative of price w.r.t. volatility) of the Black Scholes option pricing model as: ...
3
votes
1answer
308 views

Choice of epsilon for numerical calculation of vega in binomial option pricing model

I have a binomial option-pricing model (I don't think the details of how its implemented are relevant). However, when I go to calculate vega, I am essentially running the model a second time with new ...
0
votes
1answer
473 views

Which prediction market model is efficient and simple to use?

For a college project I'm tasked with implementing prediction market. Which model of it I'd better choose? I want something useful and simple enough for other people to quickly understand and use. ...
3
votes
1answer
147 views

Value options when the currency’s risk free rate is negative?

How would you handle a negative interest rate in index/equity options valuation? An example would be negative rates for short term maturities for Swiss Frank (CHF).
2
votes
4answers
2k views

Why is short term implied volatility typically higher?

Why do short term implieds move more than long term?
6
votes
3answers
227 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 ...
4
votes
2answers
991 views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
3
votes
2answers
1k views

Why do ATM call options have a delta of slightly bigger than 0.5 and not 0.5 exactly?

From the formula of the delta of a call option, i.e. $N(d1)$, where $d_1 = \frac{\mathrm{ln}\frac{S(t)}{K} + (r + 0.5\sigma^2)(T-t)}{\sigma\sqrt{T-t}}$, the delta of an ATM spot call option is ...
1
vote
0answers
162 views

Pricing a Power Contract derivative security

I'm trying to price a "power contract" and would appreciate guidance on the next step. The payoff at time $T$ is $(S(T)/K)^\alpha$, where $K > 0$, $\alpha \in \mathbb{N}$, $T > 0$. $S$ is ...
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 ...
1
vote
0answers
163 views

How to calculate a the PFE for a Swaption?

How do you calculate the Potential Future Exposure (PFE) for a swaption? Do you incorporate the dynamics of implied volatility when you are running your simulations? Is there a standard way to ...
2
votes
2answers
2k views

How to Delta Hedge with Futures?

The theory of delta hedging a short position in an option is based on trades in the stock and cash, i.e. I get the option premium and take positions in the stock and cash. In the classical ...
2
votes
1answer
117 views

Question on OptionMetrics: when are adjustments for discrete dividends needed?

Bakshi et. al. (1997) analyzes the empirical performance of some alternative option pricing models. I am interested to do this as well - hence applying different models - but I am unsure how to handle ...
-4
votes
1answer
567 views

Show that convexity of call price as a function of the strike is violated [closed]

European call options with strikes 90, 100 and 110 on the same underlying asset and with the same maturity are trading for 22.50, 18.84 and 13.97 respectively. show that the convexity of the call ...
3
votes
1answer
177 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 ...
3
votes
2answers
715 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 ...
4
votes
3answers
234 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 ...
7
votes
2answers
939 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 ...
3
votes
1answer
140 views

How do I model risks for specific short-term short calls in a portfolio with limited data?

I'm trying to do some risk analysis on a portfolio of bonds, currency, stocks and short calls. The short calls expire in approximately 15-30 days and I've only got around 20 days of pricing data on ...
2
votes
1answer
197 views

Greeks and Option Premium

If a linear sum of options is constructed such that the premium payout is zero, then does it mean that resultant greeks of the cumulated options positions will be nearly zero. For simplicity, lets ...
6
votes
4answers
896 views

Why the interest rate for put-call parity is not constant?

Usimg the put-call parity $C - P = S - K · e^{-rt}$ I tried to estimate the value of $e^{-rt}$, the present value of a zero-coupon bond that matures to 1 in time $t$: $e^{-rt} = (P - C + S) / K$ ...
3
votes
2answers
916 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 ...
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 ...
1
vote
1answer
426 views

Portfolio Greek Exposure Equations

What are the calculations for calculating greek exposures in a portfolio of equities and equity options? I think I have them but I want to be sure. Are these correct (for vanilla options)? ...
5
votes
2answers
948 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 ...
1
vote
2answers
737 views

Multi asset option portfolio risk management (greeks and FX exposure)

I am running an options book containing listed options across multiple products. I trade mostly equity and index related options - with a preference for European expiration products. I trade products ...
2
votes
1answer
350 views

Is there any evidence that an option delta approximates ITM expiry probability?

Several sources (online and offline) that discuss the delta of a listed vanilla option, state that its delta is a (guesstimate?) of the probability of said option expiring ITM (in the BSM framework). ...
1
vote
1answer
127 views

Brent Crude Data

I am trying to locate historical volatility data (5+ years) for Brent Crude? Does anyone know where I might be able to source such data?
2
votes
2answers
427 views

Why don't options traders use charts? Or do they?

Retail trading platforms typically offer equity charts but only instantaneous quotes on options. It seems like even a few minutes of historical data would be useful when entering an order. Are charts ...
3
votes
3answers
344 views

Basic question about Black Scholes derivation

In the derivation of the Black Scholes equation, the value of the portfolio at time $t$ is given by $$P_t = -D_t + \frac{{\partial D_t}}{{\partial S_t}}S_t $$ where $P_t$ is the value of the ...