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.
2,412
questions
0
votes
1
answer
56
views
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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]$$
where
EBITDA = EBITDA of the company as of the last closed and ...
1
vote
3
answers
383
views
Floor vs Receiver Swaption with Equal Strike
Let's say we have the following two instruments.
A 5x10 floor (5-year floor, five years forward) with a 4% strike on 1-year SOFR and
A 5 into 5 European receiver swaption (right to enter into a 5-...
0
votes
0
answers
82
views
Ito Process: How to calculate expected return?
On page 300 of Hull's Options, Futures and Other Derivatives
It is tempting to suggest that a stock price follows a generalized Wiener process; that is, that it has a constant expected drift rate and ...
0
votes
0
answers
30
views
Fuzzy Logic - Smoothing of payoff function: Linear vs. Sigmoid
For some options such as digital and barriers it is common to use "Fuzzy Logic" to improve estimation of value and greeks. But how / when are different functions used for smoothing the ...
9
votes
2
answers
1k
views
How we can derive the PIDE of double exponential jump-diffusion model (Kou model)?
I'm working in double exponential jump-diffusion model known as the Kou model with following form, under the physical probability measure $P$.
$$ \frac{dS(t)}{S(t-)}=\mu dt+\sigma dW(t)+d(\sum_{...
0
votes
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) ...
0
votes
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 ...
0
votes
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 ...
0
votes
0
answers
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 ...
0
votes
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 ...