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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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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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 ...
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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 ...
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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 ...
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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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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/...
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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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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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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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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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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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Far OTM calculation issue on Bjerksund-Stensland
Has anyone come across and fixed calculation issues on boundaries using Bjerksund-Stensland 2002 (Hull, Haug or Rouah implementations) ?
Thanks in advance
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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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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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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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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 ...
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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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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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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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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 do borrow rates in single-stock options affect their prices
Would following approach be suitable:
First calculate European option price (does it even make sense to do so, if we are talking about less than 30 dte?), take the diff between European and American ...
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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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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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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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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 ...
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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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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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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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How would I find correlation / association of different time series datapoints with a target variable?
the title is a bit confusing.
Functionally, I have a dataset of N stocks containing options information, short information, and earnings information for each of the N stocks.
For each unique stock in ...
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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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Bachelier Pricing Formula for Interest Rate Binary Options
Similarly to the Black and Scholes formula, I am looking to replicate Bachelier's caplet formula with two digital options: (1) asset-or-nothing (forward rate in this case) and (2) cash-or-nothing. For ...
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Volatility surface
When fitting/calibrating a option model like heston to option data, what are some useful data handling to do?
The basic thing is to remove all options with no trade/volume, but how many maturities ...
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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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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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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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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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Gamma smoothing of vanilla options
I want to ask a question about the answer provided here: https://quant.stackexchange.com/a/35211/61083. I'm wondering if there is mathematical proof as to why it is working. Meaning if I reprice a ...
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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 ...
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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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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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Delta Volatility Surface Usage to value the option
I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface?
Example
I have CME traded ...
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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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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 ...
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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 ...
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