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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12 views

Difference b/w Spot Premium and Forward Premium for FX Options

Can someone elaborate the difference between the two, and what is the typical convention used in markets? If there is a mathematical relationship. Any helpful links/guides would be appreciated as well,...
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148 views

Any good papers on Fixed Income Option pricing?

Whilst I have managed to find plenty of material on pricing of Interest Rate Options (i.e. Caps, Floors, Swaptions, spread-options, etc.), I haven't really managed to find any solid papers on the ...
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Compare equity option volatility under SOFR vs LIBOR

We know that after the big bang from LIBOR to SOFR, LIBOR will eventually disappear. This brings up one question that I do not have a clue to answer: How to evaluate derivative in a consistent manner ...
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How does a concave up volatility smile correct high kurtosis for ATM option contracts?

Theoretically speaking, if we are to assume the following: Constant implied volatility throughout all strike prices The underlying's prices change distribution is log-leptokurtic and symmetric Then ...
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60 views

Swaption decomposition - forward options and option on options

I am following through the book "An Introduction to Financial Derivatives" by Salih Neftci. According to the book, a swap can be decomposed into cash flows from forwards and options. I am ...
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71 views

What is the SVI model? [closed]

What is the SVI model? And how does one calculate its parameters?
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How to calculate greeks [duplicate]

Hey how traders calculate greek parameters when there is no formula for option price? What methods are the most popular?
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108 views

Jump diffusion simulation

I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
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Risk neutral valuation : Options on futures derivation [closed]

Recently I got a problem. It is derivation of Options on futures formula using Risk Neutral Valuation. First, Futures (Now 'F') have equation that 'F=Sexp^{(r-q)(T-t)} {S = Underlying Asset, q = Asset ...
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67 views

Is there a Dupire's Formula for put options?

Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options. If now we have the data including both call and put options, is there a ...
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Can you explain grid(or lattice) for option pricing, and explicit and implicit finite difference methods in a simple way?

I am a student learning about option pricing. I understand the concept of binomial trees, trinomial trees, black scholes and monte carlo simulation for option pricing. However, I've just had a lecture ...
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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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89 views

Monte Carlo simulation for OTM options under stochastic volatility

I'm looking to simulate the stochastic price and volatility process (Heston model) using some form of Euler method for Monte Carlo approximation of option prices. The results that I get are acceptable ...
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374 views

Bergomi: Skew arbitrage

In his paper "Smile Dynamics IV" (https://www.fields.utoronto.ca/programs/scientific/09-10/finance/derivatives/bergomi.pdf) as well as in his book "Stochastic Volatility Modeling" (...
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Black and Scholes with Jump diffusion

I don't understand how to pass from this step (only for the Poisson distribution,not the Wiener increment) in the SDE : \begin{eqnarray} d S_t = \mu S_t dt + \sigma S_t dW_t + (J-1) S_t dN(t) \end{...
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Implementing a replicating strategy from the order book

So I have futures data in an order book (one screenshot every day at 12 p.m. for one month) for various futures products (i.e. various delivery periods such as the next day, the day after and so on) ...
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Any resources or literature on interpolation schemes for future dates?

I have a whole stack of the popular option trading/modelling books (Natenburg, Sinclair, Hull, etc.) None of them however address the idea of pricing or modelling values at a point in the "future&...
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Calculate Value at Risk for floating rate note

Consider a floating rate note: nominal: € 100 000 000 coupon period: annualy remaining time to maturity: 7 years and 3 months The coupon amounts to 3.3%, the current 3M-money market rate amounts to 3....
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144 views

Pricing an Option with payoff $\left(1-\frac{K}{S_t}\right)^{+}$

Let $S_t=S_0 \exp\left\{rt+0.5\sigma^2t+\sigma W_t\right\}$ be the usual GBM model for a Stock price under the money-market numeraire. Suppose we want to price an option with payoff at maturity: $C_T=(...
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72 views

Bond price distribution if yield assumed log-normal

Suppose we assume that yields on a zero-coupon bond that matures at time $T$ follow a log-normal process of the type $y(t,T)=y(t_0,T)e^{-0.5\sigma^2t+\sigma W_t}$ under the T-forward measure. Then, I ...
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23 views

How to Show an Arbitrage Opportunity Exist From a Market-Linked CD?

A bank issues a market-linked CD that guarantees the original principal with an interest at an effective annual rate of 2%, plus 70% of the percentage gain on the ABC Inc. non-dividend-paying stock ...
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37 views

Calculate VaR using method of historical simulation

A bank invests € $1.000.000$ in a hedge fund. The last 500 daily returns can be taken from a database. The worst 20 returns are -4.58 -2.95 -2.95 -2.93 -2.17 -2.08 -2.06 -1.98 -1.94 -...
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boundary conditions in finite element method

In the appendix A of this paper, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.227.5073&rep=rep1&type=pdf, a finite element method is demonstrated to price a straddle. The same ...
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Why does higher volatility for ATM Call Option lead to a lower risk-neutral probability of expiring ITM?

This is a follow-up question on the discussion in the thread here, from which I borrow the graph below depicting $N(d_2)$ (i.e. the risk neutral probability of a Call option expiring in the money) ...
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117 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 ...
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Newbie question on volatility surface building

I am trying to build a prototype equity volatility surface for pricing european call options, as a way of learning a new programming language that I am looking at. Is there anything wrong with the ...
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Reproducing a short put position using known binomial option tree

Suppose a put option follows prices according the the binomial tree I've made and posted below and consider writing a put ($S$ is the stock value, $P$ is the put value, obviously). I want to find the ...
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Continuity of a portfolio with two options with respect to the strikes

Consider the covariance, evaluated at time $t$, between two call options written on two different but not independent underlyings $S_1$ and $S_2$ defined on the same (filtered) measure space $\left(\...
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Determine if max profit/loss on group of option legs is unlimited

Say you have a group of option legs for a symbol either for a strategy like a vertical spread or maybe an iron condor. Each with different strikes, expiration dates, etc. Without identifying the type ...
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55 views

How does volatility affect an option payoff diagram? [closed]

I am a beginner to financial mathematics, and my lecturer asked me to ponder about how volatility may affect the value of an option (as a function of spot price). For example, if an option had a (...
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26 views

How option value default adjusted in jump diffusion model

According to the doc here: http://faculty.baruch.cuny.edu/jgatheral/JumpDiffusionModels.pdf. Formula 7 specifies that the option value under jump diffusion model becomes: So when the default ...
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Quantlib simulating options with different evaluation dates

Im given a dataset of option data that looks like this. ...
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127 views

Can we model Implied volatility using GARCH?

Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used ...
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276 views

Static vs Dynamic Hedging: when is each one used?

I understand that, in Static Hedging, you don't have to keep rebalancing the offsetting position(s) while in Dynamic Hedging you have to constantly keep re-adjusting it. What I'm not clear on is when ...
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Payoff of barrier options

I was reading a research paper recently and the author defined payoffs of Up-and-Out and Down-and-Out barrier call options as max[0, ST - K]I(m < H) and max[0, ST - K]I(M > H) respectively. K is ...
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How should I interpret this Put Option delta graph?

In the following graph there's an example of Delta for a Call Option and a Put Option. I understand what this greek means and I understand why it's positive for calls and negative for puts. What I don'...
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Is this actual example of calendar arb in quotes?

From my understanding total implied variance has to be a monotonic function of time for there to be no calendar arbitrage. Stumbled upon quotes for this Monday with apparent arb (NKE Dec expiry vs Jan)...
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Can you use the SABR implied volatility in the Black Scholes formula?

The SABR implied volatility is often used as an input in Black's model to price swaptions, caps, and other interest rate derivatives. I'm wondering whether you can use the SABR closed form solution of ...
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127 views

Covariance of a simple option portfolio

Suppose that you have an option portfolio composed by two plain vanilla call options. Each option has, as underlying, a different share following a different Brownian stochastic process. The two ...
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57 views

Does a barrier breach in a geared put structured note result in greater losses for the investor vs a plain knock in barrier?

I understand how knock in barriers work. But what do geared put in a structured note mean? My understanding is in a geared put vs a regular knock in barrier, the loss for the investor is higher if the ...
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23 views

Greeks for options without bid price

It is very common to be long option without any bid price. What would be the best way to estimate Greeks for such an option? At the ask price? 1/2 of ask?
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54 views

using bid ask prices to imply bid ask volatilities

Let's say i have bid / ask feed of an option prices (across strikes and expiries, calls and puts), what is the accurate way of implying out vols from these bid / asks For eg; to get the bid vol, ...
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126 views

Vega in the Heston model

I'm trying to calculate the hedging quantities of the Heston model. I undestand that the replicating portfolio consist of one option, $V = V(S,v,t)$, $\Delta$ stocks and $\phi$ units of the option to ...
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How can cumulative delta for options over an interval be calculated?

How can a graph like on the bottom of the image be created? What information is needed? ()
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45 views

Book/Reference on LEAPs/ Long dated options

Can anyone suggest a book on pricing and trading in LEAPs / Long dated options (maturity atleast 6 months )or a generic book which covers this topic in great detail. I’m specifically looking at how ...
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166 views

Deriving the solution for European call option in the Heston Model

I'm deriving the solution for European call option in the Heston Model. I follow the original paper by Heston and Fabrice Douglas Rouah's derivations in his book The Heston Model and Its Extensions in ...
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Determining the early exercise curve of an American option

When I have found the price of an American option using, say, a finite difference scheme - how do I find the early exercise curve from this solution? Here is my idea: What I have is the price of the ...
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Replicating portfolio

I have a doubt about the replicating portfolio methodology. Example - Consider an European Call with $K=21$ and underlying with current price $S_0=20$. We assume that, at the maturity, the underlying ...
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Mismatch of periods with numeraire compared to the forward rates

In Joshi's The Concepts and Practice of Mathematical Finance Page 323--324 I believe that there may be a mismatch of periods with forward rates: Consider time partition $t_{0} < ... < t_{n}$ ...
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46 views

Collar Option K Term

I know that the value of a collar option on a stock (buy stock, buy put at $K_1$ and sell call at $K_2$) is given by $$Collar\ Value = K_1d(t,T)+Put\ Value-Call\ Value$$ My question is, why do we have ...

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