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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Constructing payoff with options
Suppose that COMPANY A has issued a special bond that does not pay any coupons. At maturity T, the bondholder receives the principal (face value) equal to 1,000 plus an additional ...
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How to get the fair value for an option with variable strike?
I'm dealing with a plain vanilla written put but my strike is linked to this formula:
$$K=(7 \cdot EBITDA\cdot Net Debt)\cdot [\%P]$$
where
EBITDA = EBITDA of the company as of the last closed and ...
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Ito Process: How to calculate expected return?
On page 300 of Hull's Options, Futures and Other Derivatives
It is tempting to suggest that a stock price follows a generalized Wiener process; that is, that it has a constant expected drift rate and ...
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Fuzzy Logic - Smoothing of payoff function: Linear vs. Sigmoid
For some options such as digital and barriers it is common to use "Fuzzy Logic" to improve estimation of value and greeks. But how / when are different functions used for smoothing the ...
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Floor vs Receiver Swaption with Equal Strike
Let's say we have the following two instruments.
A 5x10 floor (5-year floor, five years forward) with a 4% strike on 1-year SOFR and
A 5 into 5 European receiver swaption (right to enter into a 5-...
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how to use ratio spread?
If I sell more options, then my gamma risk will be more difficult to control, but if I sell too few options, then when I judge the wrong direction, I will leave the market with a loss. I try to ...
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Put-Call Parity; Time Value of Money
The intrinsic value of a call option is found by subtracting the discounted strike price from the current share price:
$IV = S - X/e^{rT}$
Put-Call parity:
$S + p = c + X/e^{rT}$
$c = p + (S - X/e^{rT}...
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implied volatility for close to expiry ATM options vs VIX
All throughout my MFE I was told that implied volatility for close to expiry ATM options is a reasonable estimate for current volatility and tracks realised vol pretty well. Then why does VIX measure ...
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Approximating implied price vol from implied yield vol?
I am wondering if there are any approximations that exist to convert yield vol to price vol? I am dealing options on SOFR futures, which can be quoted in yield and price (i.e. 3% put and $97 call are ...
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How can I price this option? [closed]
In the Black-Scholes model, I want to price the so called Butterfly option, where the payoff $P(x)$ is the following function: $P(x)=0$ if $0\leq x\leq 40$, $P(x)=x-40$ for $40\leq x\leq 60$, $P(x)=-x+...
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PnL distribution standard deviation not decreasing with delta hedging? [closed]
I am trying to write a class in python that calculate the PnL loss while delta hedging an option. If I am not mistaken, the PnL distribution should center around the value of the option, and as more ...
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Replication of the payoff of a chooser option
With numerical examples, how can the payoff of a chooser option be replicated with European call and put options?
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SOFR futures options margining
If we consider quarterly (or serial, or mid-curve) SOFR options, traded on CME. Are those options subject to margining? It is clear to me that their underlying (say, 3M SOFR futures) is margined as ...
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Implied volatility greater than realized volatility at all strikes?
It is usually stated that the implied volatility is statistically generally --- not always --- greater than the realized volatility. It seems this statement is made with regard to the implied ...
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0DTE volatility and greeks
When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to ...
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If there was a way to back out implied volatility (IV) from a stock, would it be the same as the IV backed out from an option on that same stock?
I know that it is not possible to back out an IV for a stock, because the concept of IV is based on a model with underlying assumptions applied to pricing an option.
I was thinking of why IV is ...
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Straddle Approximation - Directly from Integral
The ATMF straddle approximation formula, given by
$V_\text{Str}(S, T) \approx \sqrt{\frac{2}{\pi}} S_0 \sigma \sqrt{T}$
where $S_0$ is the current underlying spot price, $T$ is the time remaining ...
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Why a Short Iron condor payoff is showing always positive
I created a Short Iron condor on Nifty 50 index European option for 9 Nov weekly expiry on 1 Nov morning 10.30 AM (live market). It's payoff is showing always positive curve. Why ? However when same ...
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A naive approach to choose a strike
The idea is to choose a strike base on the premium and historical data to have maximum profit.
For example a selling a (European) call.
$$Profit = Premium_K - (S(t) -K)^+$$
Replacing $(S(t) -K)^+$ for ...
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Wrt speed, how optimised is QuantLib's Heston pricing class?
I have a pricing formula that is 300x the speed of the QuantLib's Heston pricing class. Is it incredibly slow?
For context, on a slow 1.6 GHz Dual-Core Intel Core i5 processor, my method can reliably ...
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Python - yahoo finance options data - volatility smile plot
I have plotted the IV of TSLA options using yahoo options data, but the scatter plot doesn't look right, can anyone advise why the plot looks like this? I would expect to see a vol smile plotted.
EDIT ...
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Analyzing the Impact of S&P Volatility Shift on ATM Straddle Sale: Calculating Loss/Gain[black scholes]
Black scholes:The 1-month implied volatility of S& ;P is 16. The slope of the skewness curve is -1 point per 1%; For example, the 99% exercise trades at a premium of 1 vol point. regarding the ...
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CMS diffusive dynamic
As I am landing on a project related to CMS option, I am wondering if one can write dynamic for CMS depending on the pricing model.
For example, is it possible to have a diffusive dynamic for the CMS ...
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Vega, square root of time, and ATM straddles
Could someone intuitively explain why for say a 1y EURUSD option -
If you buy 100 (50/leg of straddle) of 1y at the money EUR vol, that = sq root of 12 x 100 = roughly 350k of EUR vol.
If you buy 100 ...
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Is SABR model more used as an interpolation method or is used to risk manage option positions in practice?
One can risk manage option positions via sabr model (managing risks w.r.t. the sabr params), or just use sabr as an interpolation method to get black vols and risk manage option positions using black ...
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Smile Skew and Convexity Exposure
We're all familiar with the Greeks (Delta, Gamma, Vega, etc.). They provide a quantified exposure to various risk factors. But what about skew and convexity? Is there a similar standardized way to ...
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How to calculate option premium stop loss if underlying reaches a certain value near the strike price given the current implied volatility
I have sold a put option. The market is likely to open negative on Monday, the expiry of option is on Thursday. I have a certain stop loss level in my mind to exit this position if the index reaches ...
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Pricing an option with a certain payoff
Suppose an option with a payoff function
$$ \max((1+k)S_1,kS_2) $$ where $S_1, S_2$ are stock prices and $k>0$ is a constant value.
To value such an option, one would decompose this payoff function ...
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State Price Densities vs PDF of Payoffs in Ait-Sahalia (1998)
At the start of section I in the paper, the authors talk about the difference between the SPD/risk-neutral PDF/equivalent martingale measure vs the PDF of payoffs. I understand that the SPD is used in ...
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Theta using black scholes when time to maturity approaches 0
When time to maturity tends to 0, like on expiry day, denominator $\sqrt t$ in becomes 0 and the first term in the formula becomes large enough to make theta of the contract more than its premium. How ...
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Expressing Volatility Smile as One Number
Is there an accepted way in academia / industry to express the volatility smile as one number? (Not the full vol surface, but just the smile for a given option maturity: i.e. the implied vol as a ...
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Is Lookback option more path-dependent than an Asian option
Lookback option:
Path dependency comes from taken the extremum over the whole trajectory.
It is equivalent to a continuous barrier option which can be statically replicated which makes the continuous ...
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Why do we use a simple average for pricing options in MonteCarlo?
I was recently reviewing my notes on the Binomial Trees and MonteCarlo (MC) methods for option pricing. I've taken this for granted and just used the method....but I started questioning why we take a ...
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Do different hedging strategies affect the theoretical pricing of options in one period binomial model?
I just started my financial maths master and was introduced to binomial option pricing for European options.
I am slightly confused by the derivation as I saw a different version. Some straightly get ...
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In the paper "By Implication" by Jaeckel, he says that put-call parity should never be used in practic
In this paper by Jackel (2006), on page 2, he writes:
The normalised option price $b$ is a positively monotic function in $\sigma \in[0, \infty)$ with the limits
$$
h(\theta x) \cdot \theta \cdot\left(...
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What does the level of put call ratio of SPX tells you about the impending S&P 500 movement?
I have been following a YouTube channel and noticed that a high level of put-call ratio can be used to explain regardless of whether the S&P closes in the red or green.
Market closes in the green ...
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Assessing the value of risk reversal and the fly
This is important for traders.
What I'm really asking is how do we ascertain if vanna (or dvegadspot) is being valued correctly by the market?
and for the fly, fair fly value will be a combination of ...
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Best practices for building an FX volatility surface with Quantlib in Python
Generally my question is: what are best practices for building FX volatility surfaces with Quantlib?
In FX options, I would like to price structures such as risk reversals, strangles and butterflies.
...
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Is it possible to price a call option given a daily underlying returns distribution?
Apologies in advance if this problem is somewhat ill-posed. But I was thinking given the price of a call option can be formulated in terms of a implied probability density function at time $T$, would ...
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How did Jim Gatheral come up with the SVI parameterization?
I know it has nice properties relating to Roger Lee's moment formula and the Heston model asymptotics, but I am just curious how Jim Gatheral came up with this formula in the first place. I read a ...
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Volatility Mismatch in SABR Calibration
Problem Statement
Hi, I am trying to calibrate SABR on a new asset, which is not 'forward swap rate'. While using the vanillaSABR calibration, I find the parameter 'sigma' (one of model parameters, ...
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Confusion about payoff for an option [closed]
My teacher said that the payoff of a put is $\mathrm{max}(K-S_T, 0)$, where $K$ is the strike price and $S_T$ is the spot price at maturity. Why isn't it $K$ if $K-S_T > 0$ and $0$ otherwise (i.e. $...
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Selling Strangle or Selling Straddle
Assuming positive skew premium & continuously delta hedged, is selling OTM strangle always a superior strategy than selling ATM straddles (hence P&L is theoretically simplified as 0.5 * Gamma *...
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Decomposing option payoffs [closed]
Suppose an option payoff function $$max(min(S-1, 2-S), 0)$$ To value such an option, one would decompose this function, for example, as follows: $$max(S-1, 0) - max(2S-3, 0) + max(S-2, 0)$$ Now, it ...
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What would be the practitioner way of hedging jump risks?
I have developed a keen interest in volatility strategies and have implemented various approaches based on practitioner delta. This delta is meticulously calibrated using a no-arbitrage implied ...
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Using Cubic Spline with Vol Skew for Equity Options in R
I was recently attempting to replicate a part of the paper - DeMiguel, Plyakha, Uppal and Vilkov (2013), where they compute a model-free implied volatility (MFIV) quantity.
In the paper, the MFIV is ...
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What does it mean with regards to market conditions that the historical volatility is twice the implied volatility
I am trading the Indian market indices. I calculated the last three years historical volatility. Noted down 1 standard deviation of this value.
Then I took a weekly expiry of options on this index and ...
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Arbitrage between gamma and delta on smaller timescale in options selling
I have observed that sometimes (mostly for OTM options) near expiration, an increase in option price cannot be fully explained by delta and theta(given volatility is constant). The gamma spiked the ...
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Who knows what the name of this put option is? It's like a conditional Asian option, but with an upper boundary
Let $a < K < b$, then this option formula is:
$$\left(K - \frac{1}{\int_0^T\mathbb{1}_{\{a<S_t<b\}}dt}\int_0^TS_t\mathbb{1}_{\{a<S_t<b\}}dt\right)^{\large+}$$
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Practical use of Dual Delta?
I am wondering what the practical use of the Black-Scholes Dual-Delta is?
I know it is the first derivative wrt the strike price:
$$
\frac{\partial V}{\partial K} = -\omega e^{-r T} \Phi(\omega d_2)
$$...
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