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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181 views

Practical equity options pricing

To price a vanilla option, the following information are required : Strike price; Underlying price; Volatility; Maturity; Dividends rate; Repo rate; Interest rate; The strike, underlying price, ...
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2answers
227 views

How is holding an European call option equivalent to holding an asset-or-nothing call option and writing a cash-or-nothing call option?

The cash-or-nothing call option has a payoff that is equal to the strike price. All three options have the same expiry date.
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1answer
289 views

Calculating Greeks in Covered Calls?

Just want to confirm whether Delta, Gamma, Theta, Vega will be calculated in the following way? Since we own 100 shares of stock while selling a call we need to subtract greek value from one? right? ...
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3answers
1k views

How to calculate return rates with negative prices?

I'm dealing with electricity options and I'm considering the possibilty of negative prices. I want two estimate the historic volatility. However, an arithmetic mean doesn't feel appropriate and ...
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2answers
201 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 ...
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1answer
35 views

Interpretation of vega out of BS formula

I am comparing Monte Carlo estimates of VaR (using importance sampling) under both the normal and student distributions. I am also considering risk factors other than log-prices; in particular, ...
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1answer
53 views

What exotic options are exchange-traded?

There are a number of exchanges that trade vanilla Call/Put American/European options on various underlyings (equities, indices, futures). There have been some trading in digital options on certain ...
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1answer
82 views

VIX Calculation - weighting of strikes

The formula for calculating the VIX from SPX options is given on page 4 of this document: https://www.cboe.com/micro/vix/vixwhite.pdf My question is, why is the option price at each strike weighted ...
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3answers
91 views

Is it realistic to assume that the current price of a stock takes into account the probability of it going up or down in the future?

I'm currently reading the following lecture notes: http://www1.maths.leeds.ac.uk/~jitse/math2515/lecture04.pdf On the second page, under the subsection titled "The Risk-Neutral World" it points out ...
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1answer
35 views

Difference between Closing Price, Last traded price and Settlement Price for option contracts?

What is the difference between Closing price, Last traded price and settlement price ? I got the difference between Closing Price and Settlement price from previous post : The difference between ...
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1answer
51 views

Good book about replicating portfolios

I want to know if anybody can suggest me a good textbook which explains in detail and in an understandable way how to create replicating portfolios of financial instruments like options "cash or ...
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1answer
57 views

Symbols for options on gold futures

I have a historical data set containing only options on gold futures. If I print out a unique list of option symbols I get: ...
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1answer
122 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. ...
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1answer
47 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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2answers
222 views

How to price exotic options using Monte-Carlo?

I am actually trying to solve some exercise problem using Monte-Carlo and C++ for exotic options. Namely, the exotic options are geometric Asian options and discrete barrier option. It is claimed ...
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1answer
108 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
190 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
90 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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1answer
36 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
26 views

Option platforms providing eurex products

I search an option platform providing eurex products as eurostoxx 50. Can you advice me some platforms ? Thank you in advance for your answer Julien
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1answer
185 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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1answer
107 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 ...
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1answer
130 views

Constructing Volatility Smile from Implied Volatility & Delta

I have implied volatility data for call and put options (expiring in 1 month from any given date) for a particular stock. In addition, I have the delta for the options. However, I have no information ...
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3answers
264 views

What is the effect of dividend yield being greater than the risk-free rate to American options pricing?

Even though dividends are discrete, literature often makes the assumption of continuous dividends (mostly in the case of indices but the individual stocks as well). The dividend yield denoted by q is ...
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1answer
213 views

Does Implied Volatility always exist?

I am considering a simple Heston Model Market with one risky and one riskless asset. The dynamics of the riskless asset is simply $dB_t=r*B_t*dt$ The dynamics of the risky asset is as follows, $ ...
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4answers
777 views

compute sharpe ratio for options?

Calculating sharpe ratio for shares is a straight forward task: (average returns - risk free ) / standard deviation. However i remain baffled as to how to tackle the task for options, can someone ...
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1answer
416 views

Question about option theta

I have a question about a option theta. When I evaluate the option theta of near expiry put option using Black-Scholes formula given the data as follow: Index Level = 20,500 Strike Price = 20,000 ...
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1answer
367 views

Where can I get real-time equity options quotes for a reasonable price (i am not a company) besides screen scrapping Yahoo! Finance? [duplicate]

Want to have electronic access to equity options quotes in real-time. Is there anyone offering this service to the individual investor for a reasonable price? Again it must be electronic, in other ...
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1answer
116 views

Symmetry of option-implied probability density

I was wondering whether the option implied probability density of the log returns: $x = \ln\left(\frac{S}{S_0}\right)$ with S the value of a certain stock, is always symmetric ? I was asking myself ...
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2answers
172 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.
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1answer
63 views

Feynman Kac Formula for path-dependent options

Consier geometric Brownian motion: $dS_t/S_t=\mu dt+\sigma dW_t$ Feynman Kac theorem tells us that the conditional expectation $v(t,x)=E[ e^{-rT}\Psi(S_T) | S_t=x]$ can be computed by solving the ...
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0answers
34 views

Risks Associated with Option Arbitrage Portfolio

If my math is correct, if I construct the following portfolio of options the worst that I can do regardless of what the underlying does is profit $1.74 (less commissions). Is this correct? Are there ...
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0answers
33 views

Can a large OpenInt of calls cause a stock to go down?

I read forum post from another site. Which stated... ...
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1answer
94 views

Numerical Solutions for PIDE

I want to solve an exotic options of PIDE by Numerical Methods.I just focus on the integral part of PIDE and want to underestand some tips on numerical solution of how to numerically solve it. Exactly ...
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0answers
34 views

What's the risk-neutral expectation of the arithmetic average of stock price?

All Black-Scholes assumptions apply ($y$ is yield): what's $E(A_T), E(A_T^2)$ and $Var(A_T)$ where $A_T=\frac{\int_0^T S_tdt}{T}$ is the continuous-sampling arithmetic average of the stock price ...
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0answers
14 views

negative yield (interest rate) and Option Pricing [duplicate]

If i have negative yield (interest rate) can I still proceed with Standard Black and Scholes or Simple Binomial Model? any Adjustment is required to the model? how does it effect the pricing model in ...
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1answer
58 views

American put option and rising interest rate

Will a rise in interest rate always result in a lower price of an American put option?
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0answers
24 views

Intermediate Project Presentation

I would like to know an ideal plan for explaining/representing Greeks (1st,2nd,3rd) order. The topic seems to be quite vast and very interesting but not possible to cover within a 15 mins time frame, ...
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0answers
42 views

Benchmarking option pricing under stochastic interest rates

I priced a long-term option (10 or 20 years) using two different models: one assumes constant interest rates, the other assumes stochastic interest rates. Is there a way (e.g. a benchmark) to ...
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0answers
44 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
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0answers
62 views

Cointegration and variance of time series

Given that $X_t , Y_t$ are two cointegrated random processes, what can we say about the relationship between variance of the two increments $var(X_{t+h}-X_t)$ , $var(Y_{t+h}-Y_t)$ for a given ...
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0answers
59 views

variance ratio for pair-trading

I am using the variance ratio test to check whether my sequence is mean reverting in that test there is a parameter n, How in general I choose this n? or what is the meaning of this parameter? ...
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0answers
47 views

Binomial function use in Bezier smoothing

I am using the Bezier method to smooth option volatility curves, which utilised the binomial distribution. Is someone able to clearly explain the interpretation of the binomial distribution in the ...
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1answer
163 views

Binomial tree vs trinomial tree in pricing options

Very new to pricing models. Is there a general guideline when to use binomial tree and when trinomial tree is preferred? As far as I know, unlike binomial tree, trinomial tree only gives a range ...
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0answers
17 views

Principal Protected Notes

I have a few questions on the structuring of principal protected notes. Let's say that the note has a call option on the S&P500 so that it has the following payoff at maturity: $PPN_T=100\% + A ...
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0answers
6 views

Finding the price of an option that will be exercised [duplicate]

I am reposting this question because it was originally unclear, and I didn't get the answers I was hoping for. In my finance book I have the following question T-bills currently yield 5.5 percent. ...
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0answers
19 views

How discount TVaR of a put option?

Let say I want to calculate the TVaR of a put option. After I simulated possible outcomes in real-world, how do I discount the outcomes? Is there a difference if I am hedged or not? I tried to use ...
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0answers
28 views

Price a put option on a CPPI

I want to price a put option on a CPPI using Monte Carlo. I have found so far this article which prices a call on a CPPI. I was wondering if I could use the put/call parity here, and and if so, how ...
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0answers
24 views

Literature on “Risky Risky” Method

Trying to get some information/examples on a method called "risky risky" in the context of equity option/convertible bond valuation.
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37 views

Impact of Implied skew variations on future prices

I want to test the relationship between of the oil implied volatility skew and oil future prices. I'm lost regarding the method to test the relationship. I was thinking about a regression but I'm ...