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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1 answer
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State price of a stock expresed by a portfolio of calls and puts

Suppose a competitive, frictionless market provides European call options on an asset with current price $S0$ for all strike prices $K$ at market price $C(K)$ and European put options for all strike ...
1 vote
4 answers
451 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
17 votes
4 answers
13k views

What is the importance of alpha, beta, rho in the SABR volatility model?

I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
0 votes
1 answer
146 views

Covariance Matrix of Correlated Random Variable

Suppose I know or have estimated the covariance matrix for one random variable (for example an asset) and have: $$ \begin{bmatrix} <\text{spot, spot}> & <\text{atmv, spot}> \\ <\...
16 votes
3 answers
11k views

What really is Gamma scalping?

How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
2 votes
2 answers
147 views

Price Option B Knowing The Price of a Similar Option A

How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way? For example, given a 25-strike 1.0-expiry ...
1 vote
1 answer
480 views

Monte Carlo: How to interpolate Dupire's Local Volatility

I am trying to price barrier options which can have daily or monthly observations. I first calibrated by Black vols into smooth SVI vols (with linear interpolation along time in variance) to obtain ...
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0 answers
59 views

Risk-Neutral Non-Linear Option Pricing Black Scholes Model

Looking for some help on this question. Suppose the Black-Scholes framework holds. The payoff function of a T-year European option written on the stock is $(\ln(S^3) - K)^+$ where $K > 0$ is a ...
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1 answer
230 views

Maximum value of a call option proof [closed]

I'm reading Sinclair's Option Pricing and am confused by the proof for the maximum value of a call. It makes sense logically that a call can't be worth more than the underlying, and so: c <= S The ...
1 vote
0 answers
123 views

Hedging FX Risk of a fund

I manage a mutual fund where the underlying assets (or the shares i buys) are in USD, and my mutual fund is in CLP (Chilean Pesos). How can i hedge this fx risk without affecting the return of the ...
0 votes
1 answer
289 views

Option strategy Collar

I've question regarding Collar strategy (long Put with strike $k_1$ and short Call strike $k_2$ and long stock), when calculating the theoretical P&L of the collar for large up movements of the ...
0 votes
1 answer
199 views

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 ...
1 vote
1 answer
99 views

Basic option question - spx implied move per day in points

I know that an option implied move per day is vol/sqrt(252). That being said if I want to convert this in actual SPX points, am I just supposed to multiply this by the forward ? I've been told a 2/...
1 vote
2 answers
387 views

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 ...
0 votes
2 answers
110 views

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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1 answer
137 views

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 ...
1 vote
3 answers
383 views

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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82 views

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 ...
9 votes
2 answers
1k views

How we can derive the PIDE of double exponential jump-diffusion model (Kou model)?

I'm working in double exponential jump-diffusion model known as the Kou model with following form, under the physical probability measure $P$. $$ ‎\frac{dS(t)}{S(t-)}=\mu‎‏ ‎dt+\sigma ‎dW(‎t)+d(\sum_{...
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0 answers
146 views

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 ...
6 votes
3 answers
2k views

How do we hedge option vega practically?

Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
1 vote
0 answers
242 views

How To Calculate The Implied One Day Expected Return For Earnings

I am trying to figure out how to calculate the one day expected return given I have the event volatility. In his book Trading Volatility, Correlation, Term Structure and Skew, Collin Bennet (link) ...
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2 answers
112 views

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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0 answers
114 views

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 ...
0 votes
1 answer
146 views

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+...
2 votes
2 answers
126 views

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 ...
3 votes
1 answer
1k views

Forward starting options concepts

Consider $t_0<t<T$, with $t_0=0$ (today date) and the standard payoff of a vanilla forward starting call option, $F_{t,T} = (S_T - S_t\cdot K)^+$, with strike $K$. If the price of this option is ...
0 votes
1 answer
101 views

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?
2 votes
0 answers
126 views

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 ...
1 vote
1 answer
137 views

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 ...
0 votes
0 answers
57 views

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 ...
1 vote
1 answer
133 views

Valuing an electricity swap

A colleague of mine and I are debating how to price an electricity swap. Keeping in mind that electricity futures are delivered over a period of time rather than at a point in time, I maintain that ...
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72 views

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 ...
2 votes
1 answer
118 views

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, ...
2 votes
1 answer
197 views

Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?

I have been doing reading and supposedly implied volatility of ATM options with 1-2 week expiries are reasonable vols to use as your $V_0$ when calibrating a Heston model. Firstly, why would it be ...
0 votes
0 answers
74 views

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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0 answers
33 views

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 ...
1 vote
0 answers
52 views

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 ...
0 votes
1 answer
388 views

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 ...
0 votes
0 answers
36 views

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 ...
5 votes
3 answers
2k views

Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...
2 votes
1 answer
1k views

Can european call option on stock have positive theta? (assume positive interest rate)

I believe the answer is no, as minimum value of call option is S - PV(K), which can never be below S-K. The reason for the question is this paragraph in Natenberg, pg 109: Is it ever possible for an ...
0 votes
2 answers
157 views

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 ...
2 votes
2 answers
910 views

probablity expiring in the money ..basic question [closed]

Everyone says $N(d_2)$ is the probability of the option being exercised but stocks that have really high volatility have really expensive options indicating a high likelihood of expiring in the money. ...
1 vote
2 answers
3k views

Effect of Implied volatility on option delta

I am currently hedging a short put option where strike is 6027 and expiry is 30th Mar 2023. As per my understanding when option is ITM increase in volatility will decrease the delta and decrease in ...
0 votes
1 answer
102 views

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 ...
0 votes
0 answers
22 views

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 ...
2 votes
1 answer
213 views

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 ...
2 votes
0 answers
137 views

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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