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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49 views

Does a call calendar lose its entire value if underlying increases well past the strike?

If I buy a call calendar spread, and the underlying increases, both options are in the money by the expiry of the short call. So both options increase in value, but the short one increases less ...
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1answer
173 views

Convert a call spread to a butterfly to mitigate risk

I do not have a source for this (apologies), but sometimes, I hear about option traders initiating a vertical spread(short) and then converting that call spread to a butterfly spread to mitigate risk. ...
2
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2answers
540 views

Which interest rates to use for options pricing?

I am looking at the historical treasury interest rates and am uncertain which rates would be best to use for options pricing. Should I use 1 month, 6 month, 2 year? See: ...
2
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2answers
339 views

How to compute the VaR for European Call, using the delta-normal method?

I have a European call option with current stock price $S_0$, strike $K$, risk-free rate $r$, volatility $\sigma$, and time to maturity $T$ years. I assume that the stock price at time $t$, which is ...
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1answer
41 views

How to manage risk on a call calendar when underlying is falling

Let us say I bough a call calendar spread. Now, at expiry of the short option, the underlying has decreased significantly, and I am approaching my max loss(i.e both the options are close to 0). In ...
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1answer
67 views

Why vega increases further out in time

Why do back months options have a higher vega than front month options? If possible , kindly explain on an intuitive level without a lot of math.
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1answer
119 views

Why does expected price of OTM option not equal to BS price?

If I assume that stock returns follow normal distribution with drift = 0% and S.D. = 10%. In the long, if I keep investing in this stock for a year with the same capital every year for a consecutive ...
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1answer
50 views

Pricing of a call option in one period binomial model

You are given a $5\%$ call option worth $\$2.66$. The strike price $k$ is $\$41.00$. $S(0)=40$, $Sd=35$ (i.e the lower price of the stock at $t=1$) find $Su$ (i.e the high price of the stock at ...
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1answer
219 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, ...
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2answers
422 views

Why an option has sometimes and implied volatility greater than 100%?

Sometimes, in an option chain, the implied volatility of an option is greater than 100% . How is this possible? I mean, it is possible for 100$ stock to increase more than 100%, but not decrease more ...
4
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1answer
152 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
339 views

Why is the vega of an at the money option so insensitive to movements in volatility? I.e, why do ATM options have such little Vomma?

I've been trying to understand why at the money options have very little vomma. I was reading and came across a graph that showed vega as volatility changes and I couldn't grasp how the relationships ...
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0answers
67 views

Straddle neutral strategy

What does it mean to implement a delta-neutral strategy for straddle ? A straddle consists in buying a call and a put simultaneously, at the same date, on same underlying, with same maturity and ...
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2answers
5k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
5
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1answer
131 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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2answers
77 views

Option greeks: sensitivity to 1% move

In a Black&Scholes framework how can I compute the following sensitivities: to 1% move in the underlying price to 1% move in implied volatility I would like the greeks to tell me how many ...
2
votes
2answers
211 views

Is it fair to assume $(ud=1)$ in the binomial tree option pricing model?

I have discussion with my colleague on why a general assumption $$ud=1$$ in binomial tree option pricing model would be necessary? I take it a simplification of the problem, otherwise, there will be ...
2
votes
3answers
415 views

Any New Discoveries in Quantitative Finance?

It seems like the field has become stagnant in the decades following the enormously successful and influential Black Scholes model. (The original paper has been cited a staggering 25,000 times - more ...
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1answer
128 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 ...
3
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1answer
177 views

Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
2
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1answer
226 views

Some questions about implied volatilities and how to generate theoretical prices when market prices are not available

I am building a little Excel file that take some option prices in input and plots the volatility smile/surface. I have a script that reads market prices from the option chain for 3 different ...
2
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1answer
93 views

Price an option whose strike price is always lower than the future price of the security

Suppose it is known that the price of a certain security after one period will be one of the $m$ values $s_1,\ldots,s_m$. What should be the cost of an option to purchase the security at time $1$ for ...
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2answers
740 views

How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic intereset rates, a stock paying no dividends, no repo rates etc. Let C(T,K) be the price of a call with expiry ...
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1answer
250 views

Gamma is always positive on both put and call

I recently met the claim that for standard put and calls the gamma of the options are always positive. Is this a general result? I am hoping not to assume any model, especially not Black-Scholes.
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1answer
774 views

Effect of time to maturity on european put option

Let $C(K,T,S_0)$ denote the price of an European call option with strike K and maturity T on underlying price $S_0$. Assume interest rate $r>0$. Then of course $C(K,T,S_0) \geq 0$ and $C(K,T,S_0) ...
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2answers
87 views

Anybody knows the answer to this exercise found in PWIQF?

I got this question from the last exercise of chapter 2 from "paul wilmott introduces quantitative finance" book. Appreciate your help.
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1answer
135 views

Asymptotic behavior of theta of vanilla call option

It is well known that the theta of call option is always negative. Also, the theta of (at the money call option) goes to infinity as the time approaches to the maturity. On the other hands, (ITM and ...
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2answers
160 views

How market making in Index options is done?

I have been thinking about this one for last couple of days. With options on share we hedge on cash and the underlying equity as per Black-Scholes formulation. But I am confused on Index options. ...
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1answer
109 views

Moneyness and option prices

I'm attaching stock prices from CRSP to a dataset of option prices in order to compute the option moneyness. I'm wondering whether I should adjust the underlying prices taking into account splits and ...
1
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1answer
165 views

How to calculate the probability of 2 options ending in money with different expiration dates?

Lets say I make a trade that consists of buying one put and 2 calls of the same underlying but with different expiration dates and different strikes. Example trade: ...
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1answer
175 views

Historical Implied Volatility Calculation

I'm trying to calculate implied volatility for the FTSE 100 for the last few years. I have all the end of day data from LIFFE for the last few years. I have combined the data by weighting the ...
4
votes
1answer
216 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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2answers
379 views

Which risk free rate is assumed by market when pricing american options?

I'm just started with finance, so maybe my question is dumb or answered elsewhere. Please guide me to relevant materials. According to put-call parity more time to expiration means more difference ...
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3answers
494 views

forward implied volatility skew

I would like to calculate implied forward volatility skew. I have stochastic volatility monte carlo. What kind of payoff do I need to price and how to use Black() formula to calculate the implied ...
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0answers
57 views

Opposite of hard to borrow?

If market participants are certain a stock will suffer a huge decline, the shares will become hard to borrow and an interest fee will be applied to borrow the stock. This interest fee eliminates the ...
4
votes
1answer
191 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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votes
2answers
256 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 ...
2
votes
1answer
81 views

When $C(K_2) = C(K_1)$ for call options with the same expiration date

The exercise is to show $C(K_1) \geq C(K_2)$ where C(K) denotes the value of a call option on a stock price S with strike price K. We assume the expiry is the same for both. I have proved this by ...
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1answer
815 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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1answer
114 views

Delta formula for FX vanilla option

What value do you use for annual dividend yield? It does not apply in case of FX.
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3answers
206 views

What is the name of this product?

Consider the payoff =$S_T1_{S_T>K}$ where $S_T$ is the asset price at maturity. What is this type derivative called? and is it a liquid option?
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1answer
51 views
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2answers
188 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. ...
3
votes
1answer
80 views

Binary option expression

Given r=0, σ(K)=const Binary=lim┬(ε→0)⁡〖((C(K,σ(K))-C(K+ε,σ(K+ε))))/ε〗 What is the analytical expression for the binary option value? σ(K)=const Therefore, Binary=lim┬(ε→0)⁡〖((C(K)-C(K+ε)))/ε〗 ...
3
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2answers
173 views

C# - Using Black Scholes Newton returns NaN occasionally

First caveat: I'm a programmer doing this for a client, and my knowledge of options probably has holes in it. So be a little forgiving here. =) The Issue: When I run Black Scholes Newton against ...
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5answers
3k views

Best way to store hourly/daily options data for research purposes

There are quite a few discussions here about storage, but I can't find quite what I'm looking for. I'm in need to design a database to store (mostly) option data (strikes, premiums bid / ask, etc.). ...
0
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1answer
42 views

Normal vol - convention

apologies for the simplicity of the question, but I was wondering: what is the quoting convention for normal (bps) volatility? Say I have the following time series of data: Date Close Abs Change ...
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1answer
283 views

What is the formula for beta weighted delta and gamma?

I am trying to calculate the beta weighted delta and gamma for a portfolio of options of different underlying stocks, but I can't seem to find the correct formula. Can someone point me to it or a ...
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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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1answer
495 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 ...