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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How to fit (find $u$) in the binomial options pricing model?
In the binomial tree options pricing literature, I see frequent reference to the definition that
$$
u = e^{\sigma \sqrt{n/t}}
$$
I think I understand the model, but how do we derive this, i.e. how do ...
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Implied Volatility Discrepancy in American Options - Mathematical Reasoning?
I've been analyzing Tesla stock American options data and have observed an interesting pattern that I'd appreciate some help understanding.
For this analysis, I obtained the Implied Volatilities (IVs) ...
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Black-Scholes formula is a (probabilistic) convex combination
[![enter image description here][1]][1]A call price is bounded when $\sigma\sqrt{T}$ goes to $0$ and $\infty $ by:
$$C_{inf} = e^{-rT}[F-K] \leq C \leq C_{sup}=S $$
Now a simple rearrangement of Black-...
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Methods for tracking option open interest intraday
It is my understanding that open interest option values on financial websites are a reflection of a snapshot value each day. Is anyone aware of methods for estimating intraday open interest, or aware ...
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Is American put Gamma always greater than the European one in the non-early-exercise domain?
Consider a pair of American and European puts with the same specifications except the former has the continuous early exercise right. Has anyone plotted the Gamma's of both as functions of the ...
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Finding upper bound for portfolio made from European call / put options
I tried finding upper bounds for each component in terms of E_1 using the put call parity but couldn’t get the correct answer.
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Methods to estimate Options volume
I need to build a Liquidity Risk report at my intern job. There, I consider an MDTV90 (Median Daily Traded Value for 90 days, a measure of liquidity) for each asset we trade to find how many days we ...
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Understanding the adjustment $(u/r) p$ in the binomial options pricing formula
I'm reading Option Pricing: A Simplified Approach and have a question. Assume the binomial tree model for the stock. So
$n$ discrete time periods
$S$ is stock
$C$ is call
$K$ is strike
$u$ is upward ...
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Tail Risk Hedging for Public Pension Plan
Very simplistically, ERISA rules require corporate pension plans to use market rates to discount their liabilities. If interest rates go up, the value of their pension liabilities goes down. Since ...
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Discounted price of an option
If the discounted price of any asset is a martingale under risk neutral measure, why is $E^Q[e^{-rT} (S_T-K)_+ | F_t]$, not merely $e^{-rt} (S_t-K)_+$?
This is something I wanted to clarify, since ...
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Implied Volatility Surface Interpolation for fixed moneyness and maturity on each day of the calendar
I'm new to quantitative finance and interested in performing a PCA on the implied volatility surface. However, my dataset displays certain point changes over time. As a result, I need to interpolate ...
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Is there a general approach to predicting future (vanilla) option prices in practice?
I realize that this question may be verging on asking for the proprietary/"secret", so if suggestion of a general approach that doesn't divulge details isn't really possible, I understand.
...
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Decompose Option price into greeks
I am trying to decompose option prices into various greeks and trying to see if I can recover option prices from various of its greeks.
At the start of certain time ...
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interest rate, dividend rate data for black scholes model [duplicate]
I am working on a project to build an implied volatility curve for SPX options. But I am stuck with finding interest rate and dividend rate data for all maturities. Any recommended resources?
Thanks!
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Bitcoin sell call options margin
I would like to know why on Deribit the margin requirements for selling call options is so much higher than selling futures.
It’s only about liquidity or there are other reasons?
I guess there are ...
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Is there a strategy to increase the granularity of a deep in the money options contract?
My aim to get as close as possible to a "mini" deep in the money options contract. But mini contracts aren't generally available and buying regular 100 packs of high priced stocks is ...
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Floating Strike Geometric Averaged Asian Option Pricing
How can I use the risk neutral evaluation to price an asian option with floating strike using the continuous geometric average? I have tried searching for ways to do it but have found almost nothing.
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Bloomberg FXFM: what is the point of knowing risk neutral probabilities?
Among other things, Bloomberg FXFM function allows you to check risk neutral probabilities for currencies. For instance, you can check the probability of the euro depreciating 5% vs the dollar in 6 ...
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Binomial Option Pricing [duplicate]
We are currently working on the "standard" binomial option pricing. If the market agrees that a specific stock will raise by, let's say, 90% next period. At first glance, this seems to have ...
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In the CRR model, describe the strategy replicating the payoff $X=(S_T-K)^{ +} +a(K-S_{T-2})^{+ }$ for $a \neq 0$ [closed]
In the CRR model, describe the strategy replicating the payoff
$X=(S_T-K)^{ +} +a(K-S_{T-2})^{+ }$ for $a \neq 0$
$X$ consists of two parts:
European call option with strike price $K$ and expiration ...
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What is the correlations between the Wiener processes in Heston Model?
In Heston Model we have two Wiener processes: One for the asset price, the other for the volatility. The model assumes a correlation $\rho$ between the two processes.
I ask what nature this ...
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What is the risk neutral expectiation of an option price given a move in spot?
Lets say we have a volatility surface for the SPX at time t with spot S. We consequently know the price of some call option at maturity T with strike K. What is the risk neutral expectation of the ...
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How to price very short dated options?
I was wondering if there is any industry standard in pricing very short dated options, from say 6h options down to 5 minute options.
My thinking is that as time to expiry gets shorter and shorter, the ...
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Questions on options cost of carry, and relationship to futures cost of carry
I'm trying to grasp what exactly the effects of higher ongoing interest rates are on holding calls/puts. I am not asking what the effect of a change in interest rates is on call/put prices.
I'm ...
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Joint SPX and VIX calibration - volatility surfaces construction
I am currently researching the joint calibration problem of SPX options and VIX options. A question that comes to mind is the construction of each assets respective volatility surface.
In the articles ...
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What is the Time Value of European Options if r=0? [closed]
As I understand it, time value for European options is as follows:
What if r=0? Then puts should behave the same as calls, right? Would the time value always be nonnegative or could it be negative?
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Best tool to find an optimal option? [closed]
I like to sell uncovered put options, using my valuation of the company as the strike price. I'm looking for a tool that takes stock identifier and strike price as input and outputs the optimal ...
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Free historical data for options [duplicate]
is there a way to get options historical data for free or for a cheap price, let's say 2 years at least for both EOD data and hourly ones for just one underlying instrument such as sp500? Or ...
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If American Options always have positive time value, how can it be optimal to exercise an American Put early? [duplicate]
r > 0. I understand that money today is worth more than money tomorrow. So if volatility is 0, it's better to take the money today. But I don't understand how to square away the following:
Time ...
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Is Nassim Taleb wrong about his DdeltaDvol dynamics in his Dynamic Hedging book?
if you're long OTM calls, an increase in vol would increase your delta (converges to ATM) and if you're long ITM calls, increase in vol would decrease your delta (converges to ATM as well). So OTM ...
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Comparison of the American and European call deltas
Suppose the interest rate is zero. A stock with price $S(t)$ at time $t$ pays only one dividend at time $t_1$ such that $S(s_+)=S(t_1^-)q$ where $q\in[0,1]$ is a constant. Consider a European call and ...
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Saddlepoint approximation when CGF is approximated
According to the saddlepoint approximation, if the cumulant generating function $K(t) = \log E[e^{tX}]$ of the distribution of the random variable $X$ exists and is known, then the density $f(x)$ of $...
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Does skew flatten with a decline in volatility?
In Trading Volatility by Bennett, he says:
If there is a sudden decline in equity markets, it is reasonable to
assume realised volatility will jump to a level in line with the peak
of realised ...
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How to calculate expected value for an underlying contract and expected value for an option?
In Sheldon Natenberg's Options Volatility & Pricing, he writes:
There is an important distinction between an option position and an underlying position. The expected value for an underlying ...
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Quantlib - bond with capped coupons
Using QuantLib I want to price a Floating rate bond whose coupons are capped at some rate.
I understand I could price the coupon caps separately and then add that to a zero-bond.
However, I've noticed ...
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Popular treasury futures bond options volatility surface model/s
I am looking for volatility surface parametrisation model used for treasury futures bond options. I know that most popular for options on equities its SVI, on FX its Vanna-Volga, on rates its SABR. ...
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Could a certain Volatility Surface generate two options with different strikes but the same Delta?
Is it possible for a volatility surface $\sigma(K,T)$ results in two options (both call or puts) with different strikes, but the same Delta, i.e., $\Delta(K_1,\sigma(K_1,T);S,T,r)$ = $\Delta(K_2,\...
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Intuition behind calendar spread max loss
With a calendar spread (buying back, selling front), max loss is defined as some variant of "maximum potential loss is the cost of opening the trade (Premium Paid − Premium Received = Total Debit)...
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How to improve fit in American options vol surface?
I am trying to model the volatility surface of index etfs (spy, iwm and qqq). I am using the CRR model with discrete dividends and the spot model. I find that for some cases there is a noticeable ...
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Pricing the embedded option in a callable floating rate note
From my understanding, I know that we can decompose a long callable bond into a long vanilla bond and short receiver swaption. However, I do not understand, how could I separate or calculate the ...
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How to properly weight fair value, theta, and cega in a multi asset model?
I'm working with a multi-asset worst of model and the outputs are FV,d1,d2,g1,g2,v1,v2,cega, theta.
Its easy to assign proper delta, gamma, vega to the respective asset1 & asset2, but how would ...
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Implying a probability distribution from option prices [duplicate]
I was reading this article, when I came across this text:
Without using a complex options pricing model, one can use intuition
to translate option prices into implied probabilities. For instance,
the ...
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Calibration of Local or Stochastic Volatility Models to Prices vs Implied Volatilities
As the title suggests, what is the difference between calibrating an option pricing model (say the Heston model) to market option prices instead of computing their implied volatilities using Black-...
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What is the reason for adding 0.5 variance when calculating the ATM DNS of an option?
Why is an Option ATM DNS (Delta Neutral Straddle) strike calculated using exponential value of (rate + 0.5 variance) * t. For ATMF (At the money forward), the rate time is used as the value in ...
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How to derive numeric option VaR with delta-vega normal approach?
For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by
$\Delta C=\delta \Delta S+\nu\Delta\sigma$,
where ...
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Getting incorrect options data with IB API. Missing real time market data subscription?
I'm having a problem getting options data with IB's API. The data seems not to be correct. In my code I'm getting some 0DTE call options for the Mini SP500 March Futures contract and printing their ...
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What shall I do to make my delta neutral? [closed]
Suppose that yesterday I shorted some call and put option contracts of an underlying and I had a neutral delta. This morning, I have a positive delta, and I want to keep my delta neutral. What do I ...
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How to simulate a delta hedged option strategy
I'd like to do a montecarlo simulation of a $\Delta$ hedged strategy (long OTM call) to see how the PnL distributes on cases like:
$\sigma_{bought} < \sigma_{realized}$
$\sigma_{bought} > \...
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Heston formulae and characteristic function for FX options (or dividend paying yield)
I've seen the formulae for Call valuation with the Heston model for non-dividend paying Stocks.
How should I modify it to use it in an FX pair (which has two risk free rates: local currancy rate $r$ ...
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Shape of FX Volatility Surface
I'm familiar with the volatility surface for equity options with the smile/skew dynamic and flattening with increased maturity, and the explanation/intuition behind its shape. However, today I came ...
