# 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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15 views

### Financial engineering and risk manament [closed]

Quiz Instructions: Option Pricing in the Multi-Period Binomial Questions 1-8 should be answered by building a 15-period binomial model whose parameters should be calibrated to a Black-Scholes ...
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### Option that never expires

I have been struggling with the problem below for quite some time now. I really don't know how to approach it. All I could think of is to use the Black-Scholes formula with $T \rightarrow \infty$, ...
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### Intuitive explanation of put option pricing based on put-call parity

Assuming no dividends, the put-call parity equation says: $c + \mathrm{Ke}^\mathrm{-rT} = p + S$ where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current ...
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### Why is the liquidity of ATM stock options often relatively low even if the underlying security is being traded in large quantities

I am currently trying to learn more about options trading and option strategies. One thing I have noticed recently is that for a lof of stocks I look up on yahoo finance often a very low open interest ...
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### Do basket options have a closed form valuation formula?

Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ...
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### Early exercise premium with discrete cash dividends using integral approximation

From my understanding, we have to integrate $N(d1(S_x-D,B,t))$ on both asset-price and time-space to derive the Early Exercise Premium $EEP(B,t)$ on each $t$ before the ex-date to get current early ...
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With a payer swaptions delta and gamma is there a method for approximating pnl for a given move in underlying swap rate? (An equivalent to the Taylor expansion for a vanilla call) Thanks!
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### What is volatility trading? [closed]

What is meant by volatility trading? Is it trading 'options'? Aren't options meant to leverage stock prices, and not their volatility?
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### Ratio of the same process at different times

Suppose I have an adapted process $X_t$. I have available option prices on $X_t$ for a range of strikes and maturites. In particular, I have $$C_0(K, T_1) = D(T_1)\mathbb{E}_Q[(X_{T_1} - K)_+],$$ ...
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### Options conversion/reversion arbitrage [closed]

I'm trading bitcoin option and i'm trying to find arbitrage opportunity with a synthetic short/long and a long/short future position. The options are europeans style and settled in BTC. The contracts ...
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### Why does implied volatility decrease without a change in stock price?

I was lookin at some stocks and find that implied volatility changes without the stock price moving too much. What are the causes?
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I would like test if there are "crash risk premia" priced into out-of-the-money puts. My initial thought was to create a portfolio with a short positions in (deep) OTM put options and a long ...
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### Option price quantlib

I am lookin at https://github.com/lballabio/QuantLib/blob/master/Examples/EquityOption/EquityOption.cpp . I want plot a graph of the option price for different underlying prices. Other than changing ...
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### Hedge robustness of the one factor Hull White model

I recently came across a quote in a book: "All single factor models share the limitation that shifts in curve levels cause shifts in the package of vanilla options that are a good hedge for the ...
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### What kind of option would best be suited for a price based algorithm?

So say I wanted to make money off of a simple RSI-MACD algorithm on SPY (ofc this may not necessarily make money, but let's say it does). I'd like to leverage my returns using call and put options, ...
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### Asian option sensitivity

I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM. Is ...
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### Market Maker option's pricing with reference spot

When a option's market maker receives a quote from a broker, usually the underlying spot prices is locked with a reference. Let's suppose the following example: Broker: "Buy 10k call 2800 of ABC ...
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### What put options would the Universa Tail Fund have bought?

According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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### How Are Option Model Assumptions Justified In Practice

I am reading this article, and I am wondering how comments like there may be a 50/50 chance that the underlying asset price can increase or decrease by 30 percent in one period. are reconciled with ...
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### Predict option IV volatility when I have stock price and previous and next day price

If I have data for IV for the previous day the next da and the stock price in intraday format , can i calculate the option price in intrday format?
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### Can you simulate an option position at a strike when that does not exist

Is there any way to simulate buy an option at a pric of x when that price is not available to buy ? If x-3 and x+3 exists, how do I buy it at price x?
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### Can “Turbo warrants” be priced using the Black & Scholes model?

I am trying to model the pricing of an asset called a "Turbo warrant", which to me looks a lot like a Down-and-Out Barrier option with leverage. When the price of the underlying asset hits a ...
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### Power Options & Forwards on Stock Squared

Short story: the process for Stock price squared is not a martingale when discounted by the money-market numeraire under the risk-neutral measure. How can we then compute derivative prices on $S_t^2$ ...
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### How to calculate Greeks for leveraged Barrier options?

I am wondering how to calculate option Greeks for Down-and-out barrier Call options with leverage. The option characteristics are as follows. The buyer of the option pays a fraction of the spot price <...
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### Confusion about replicating a call option

Assume standard Black-Scholes model, $$dS(t)=S(t)(rdt+\sigma dW(t))$$ where $\sigma$ is a constant and $W(t)$ is a Brownian motion under the risk neutral measure. A call option is replicable, so if we ...
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### Why are these deep in-the-money FLEX options seemingly bought at a discount?

98% of the initial reference value is .98 x 267.88 dollars, which equals 262.52 dollars. However, the market value of each call contract they purchase is 247.42 dollars. How are they purchasing these ...
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### VIX vs S&P: Drift in the hedging residual?

I am looking at the daily returns of the VIX index (dVIX ) and the daily returns of the S&P 500 (dS). I am running a linear regression (using 0 intercept) and get a regression slope of -1.4, i.e. ...
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### How do I achieve a Long Gamma, Short Theta Exposure?

How I understand it is that if I: Sell OTM near dated put which will pay high theta and have low gamma Buy ATM long dated put which will have low theta and have higher gamma However, if there is a ...
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### Do barrier options have closed form values for Greeks?

This may be quite simple but I was wondering if barrier options, and more particularly up-and-out European call options have closed form values for the Greeks?
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Assuming we have the fair value of the July straddle on a certain strike, what would be the implied July-Oct forward vol if an order comes in to sell the July-Oct Put Spread (on the same strike) for a ...
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### Summary of Pricing Options of Log-Normal Claims Using Black's Formula

Cross posted from here. Let $B$ be a $Q$-Brownian motion and $X^{s,x}$ given by $$dX_t = X_t(\mu_t dt + \sigma_t dB_t),\quad X_s = x$$ for $\mu, \sigma$ deterministic. Let $\mu_{s,t}=\int_s^t \mu_u du$...
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### Why do replicating strategies delta hedge?

We have a simple BS-market of one risky asset $S_{t}$, a bond $B_{t}$ and a digital option $X$ on the risky asset with value process $V(t,S_{t})$. I was able to derive $V(t,S_{t})$ using risk-neutral ...
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### How is the implied risk neutral density affected when changing numeraire?

For example i would like to price \begin{equation*} E^{Q} \left[ e^{-\int_{0}^{T}r_{s}^{cur}ds} f \left( S_{T_f}^{cur_1} \right) | \mathcal{F}_{0} \right] = B_{cur}(0,T)E^{Q^{cur}_{T}}[ f(S_{T_f}^{...
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### How to understand broken wing butterfly option strategies?

I feel very confused about the greeks analysis for the broken wing butterfly strategy. Let's say for the stock ABC, we enter into a such strategy: we long a put option with strike $k_1$ and another ...
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### Are there noticeable jumps in index options price due to systematic hedging of structured products close to big expiry dates?

I am looking at investigating factors that will cause jumps in index options prices close to big expiries in the name. I imagine systematic rebalancing of structured products will have a large impact ...
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### Is this a new way to profit from earnings releases using long straddles?

How much can I reasonably make if I buy a long straddle just as soon as earnings release day is announced and ride the rise in implied volatility along with any movements till the earnings release ...
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### Hand coded algorithm for tangent algorithmic differentiation

I'm looking for a way to hand code the algorithm for the forward/tangent mode of algorithmic differentiation to calculate option Greeks with Monte Carlo simulations. The computational power is very ...
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### Should I hedge this spread with a spread option or an insurance product?

My firm generates electricity from wind. Accordingly, most of my generation takes place at night, when prices are low -- and, due to congestion / oversupply, often sharply negative -- so much so that ...
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### Option data analysis

This question is regarding the following tweet: https://twitter.com/yuriymatso/status/1281730109141954561 How was the original tweeter able to know that "Someone made a ...
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### Intution behind buying the option when implied vol seems low

Hi All: I've started reading "volatility trading" by Euan Sinclair and it's a very nice book. It's not so theoretical but instead focuses on the practicalities when dealing with trading ...
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### Implied Vol Smile: from Calls, Puts or Both?

This might be a simple question, but I couldn't find the answer anywhere: is there a separate Volatility smile (and surface) based on Calls and a separate Volatility smile (surface) based on Puts? Or ...
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### Realizing profit with Gamma Trading doubt

Lets suppose we have a delta-neutral portfolio and that we want to trade the gamma. If we are long gamma, we can profit from every rebalancing to keep the portfolio delta-neutral. Lets suppose the ...
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### Confusion about optimal choices with exotic options

With exotic options, holders usually face choices at certain times. In my understanding, the price of the option is determined by assuming the optimal choice is taken and computing the discounted ...
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### Confusion about American style option

In American style exotic options, the holder is often faced with choices at certain times during the life span of the option. Following the/an optimal choice allows the user to maximize the value of ...
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### How does most Forex options work? What is the most liquid or popular type of forex options?

For the "mainstream" forex options for example those (in the size of bn) posted on this site: https://www.forexlive.com/orders/!/fx-option-expiries-for-thursday-july-02-at-the-10am-ny-cut-...
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### Higher moments of a straddle

Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are: Similarity, for a call it is as follows: where and ...
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### “The potential gain of a Call Option is always incorporated in the Option's price” - Why is that?

I've heard this but I don't understand why. The demonstration of this is that the Ask Price of a Call Option is always higher than the difference between the Strike Price and the price of underlying ...
I don't see why would rates be considered as deterministic when trying to price $\mathbb{E}^{Q} \left[ e^{-\int_{0}^{T_{f}}r_{s}ds} \left( S_{T_f} \right) | \mathcal{F}_{0} \right]$ I would like to ...