Questions tagged [european-options]

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How to estimate or determine leverage from strike price on ITM call option? [closed]

In this text 4x leverage is mentioned: "ITM call options have a strike (X) below spot price (S). ITM call option position is determined by aiming for ~4x leverage. The position size is set at 33%...
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Contradictory arguments for ATM/ITM/OTM option demand

I am trying to understand which of the options have the most demand, and found this discussion here. The arguments presented are as follows: ATM is more liquidly traded than ITM/OTM because they are ...
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Why is this inequality strict for arbitrage argument for European call?

in the notes about arbitrage arguments I am reading, I notice the statement We can also see that $$C^E_t>(S_t-K\mathrm{e}^{-r(T-t)})^+$$ Notice that the inequality holds STRICTLY! I don't ...
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Extension of CRR model

I'm considering an extension of the binomial model where the risky asset can take three values at each node, that is $ S_{t+1}=\left\{ \begin{array}{ll} S_t\cdot u\\\nonumber ...
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Why do we worry about the bid/ask spread when pricing option in incomplete market?

Several resources I saw introduce the notion of bid/ask spread when trying to price options in incomplete market, I don't understand why the notion is introduced since we are interested on the price ...
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Are European call and put option useful ? [Cox-Ross-Rubinstein model]

I'm new to the world of option market, but after having studied CRR model I'm wondering if European call and put option are very useful since a talk with my professor that piqued ma curiosity. In the ...
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Model-Free Implied Volatility: Data of Expired Options and Bond Price

I am attempting to calculate Model-Free Implied Volatility for several equity indices (S&P500, NASDAQ100, CAC40, FTSE100, DJIA, EUROSTOXX50, NIKKEI225, NIFTY50). I wish to get historical data of ...
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2 votes
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Expectation of Product of two European Option when vol smile exist

Currently I'm thinking about how to calculate the expectation of the product of two euro option, which is $E[(S_T-K_1)^+(S_T-K_2)^+]$ I can fit some parametric vol model from the market listed option ...
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Option Chain Simulator Using Historical Index Future data, VIX, Implied volatility for Calculation ( Pls Review the Idea & give your suggestions )

Recently I started trading in options, for Learning purpose I am Planning to Create old European Option chain like previous week or last year particular entire week Weekly expire option chain with the ...
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4 votes
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Caplet stripping in the bwd-looking RFR world with/without maturity adjustment

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for ...
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What is the meaning of an implied volatility of an Asian option?

Suppose that an Asian option is quoted OTC in terms of its implied volatility. What is the meaning of an implied volatility in this case? Is it an implied volatility of a vanilla European option with ...
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Proof of Calendar-Spread-Inequality

The Calendar-Spread-Inequality compares the prices of two European Call Options on the same underlying non-dividend-paying stock, but with different maturities $T_1<T_2$. Denote the value of a call ...
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3 votes
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how does margin affect the Option Price when Selling an Option

Currently I'm thinking the effect of margin. When selling an option, you need to pay margin everyday and mark to market. In most exchanges, margin is overcollateralized. But when buying a option, you ...
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Assymptotic behaviors of European options

In some of the numerical works on Black-Scholes generalized models, the boundary conditions on the truncated domain taken from the asymptotic behaviors of European call options, which is given by $$\...
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Volatility of American vs European Stock option return

Let's say that I hold an American Call Option (ACO) and an European Call Option (ECO) in my portfolio on the same underlying, with same strike price and same maturity date. Given that I hold both ...
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Find the value of put option using a two-period binomial model

I've been asked to find the price of a two-month European Put Option with strike price $£40$. The price at $S_0=£30$, this can move up to $£40$ or down to $£25$ ($1/3$ chance to go up, $2/3$ chance to ...
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2 votes
1 answer
172 views

Why is call option value same as portfolio value at all times in Black Scholes model?

Following is a part of the text from Steven Shreve Stochastic Calculus for Finance II, for pricing the European Option in Black Scholes model. The argument is that today I start by selling a European ...
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What is the intuition behind a positive theta for European long puts?

I've googled extensively for an answer to this question. Very similar (if not identical) questions have popped up in this same website (example) but I never find the answers to be clear and/or precise....
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Valuation of non-deliverable option

What is the difference between valuation of deliverable and non-deliverable European options? I am not asking settlement-wise, but daily valuation. Will Black-Scholes be used for both?
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Relationship between VIX and Vega

Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is ...
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how can properties of transition matrix be applied in the transcation cost of option

I am currently reading the PP BOYLE's article ' Option Replication in Discrete Time with Transaction Costs' written in 1992. Here is one place i couldn't figure out: Where does that $\widehat{p}$ ...
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2 votes
2 answers
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Is there some reason for volatility smile minima to be displaced from ATM?

I am analyzing some options data and I see that the volatility smile has its minima a few strikes higher than the current traded price (about 2.5 % higher than spot). I have checked my data thoroughly....
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Why is implied volatility often higher for OTM/ITM european call options than ATM? [closed]

I am working on some Black-Scholes stuff and currently investigating implied volatility (IV). I understand that the typical volatility smile can be viewed as a criticism of the assumption about ...
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1 vote
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HNGARCHFIT in R (No standard deviations or P values printed)

When I estimate an HN-GARCH model using the hngarchfit() from the fOptions package in R, only the coefficient estimates are printed. There are no standard deviations or P-values printed. Does anyone ...
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European call option lower bound derivation by Black-Scholes formula [closed]

Derive the lower bound of european call options: $$C(S, t)\geq[S-e^{-r(T-t)}K]^+$$ I know how to derive it using put-call parity, but is there any way to derive from Black-Scholes formula?
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How to approximate a delta using monte carlo methods and finite differences via Higham's book?

I'm currently taking a Mathematical Finance module at University and one of the recommended texts is “An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation” by D.J. ...
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Reason why a European binary call should be worth half of its American counterpart when driftless and out-of-the-money

Exercise 11 of chapter 8 of Mark Joshi's "The concepts and practice of mathematical finance", asks to compare prices of an American and a European digital (binary) calls when out-of-the-...
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Price of european call option for different strike prices

Consider two european put options with strike prices $K, J$ with $K<J$ and maturity $T$. Then the no arbitrage assumption implies $P_{K}(0)<P_J(0)$, where $P_K(0)$ denotes the price of the put ...
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Forward Index Level in VIX calculation

The VIX white paper (https://cdn.cboe.com/resources/vix/vixwhite.pdf) step #1 (page 6) says the the Forward Index Price is calculated as: F = Strike Price + e^RT x (Call Price - Put Price). Why doesn'...
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Intrinsic Value of European Options [closed]

I have a question regarding the intrinsic value of an European option. I use the following notations: $S_t$ price of the non dividend paying stock at time $t<T$, $T$ is the maturity, $r$ risk-free ...
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Prove the Euro call option value has positive relationship with the risk-free rate under discrete time model (Binomial tree model)

Could anyone show me how to prove that the European call option value has a positive relationship with the risk-free rate in a two-step binomial model with strike price K and different risk neutral ...
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Barrier Reverse Convertible

I am a finance student and during my free time I try to understand more financial products. Today I have found a term sheet for a specific type of barrier reverse convertible but I couldn't understand ...
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1 vote
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Is this the PnL you would expect to see for a hedged call option portfolio? [closed]

You are a market maker. Charging no commission, your only aim is to remain market (delta) neutral. Therefore you construct a portfolio of the form: $$\Pi = -C - w_{1} B + w_{2} S$$ where $B = K \cdot ...
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3 answers
154 views

Intepreting European call option when expiration approaches to infinity

Assume that dividend = 0, then the price of call option is $$ C = S\cdot P_{s}[S(T) > K] - e^{-rT}K\cdot P_F[S(T) > K] = SN(d_1)-e^{-rT}KN(d_2) $$ where $P_s[S(T) > K]$ = Probability of ITM ...
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3 votes
0 answers
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Intraday "Time to expiration" for Black-Scholes on the expiration day

In Black-Scholes, T is the % of year, how do we calculate T intraday on the expiration day? Does the expiration happen at the exact moment of that trading session? For example, for SPXW options that ...
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1 answer
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How to price an European put option using binomial model with dividend yield?

The initial stock price (S0) is 45, the stock volatility is 0.20 (20% per annum), and the risk-free rate is 0.02 (2% per annum). Consider a European put option whose strike price is equal to 30, with ...
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Option where option writer determines type of option to give to holder

I am currently looking at an exotic option that allows the holder, at some time $\tau$, to receive either a call or put — the choice of which is decided by the option writer — of which both have the ...
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1 vote
1 answer
274 views

Hull's book - Futures option's rho

In Hull's book (9th edition), on page 420, in table 19.6, it says rho of a European call on an asset with yield $q$ is $$KTe^{-rT}N(d_2)$$ Below it says we can compute greeks of European options on ...
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0 votes
1 answer
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Maximal increase payoff

I am interested in the following problem. We have a Multi-Step Binomial Model with discrete time $T=1,\dots,n$. We also assume that the stock $S_t$ is a martingale and there is a risk-free bond with $...
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1 vote
1 answer
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Investigating how rational price of European call option changes [closed]

Let S(0) = 100 be the initial price of the risky asset. Consider a European call option with exercise price K and expiry time T = 1 (year). Consider several binomial models and investigate how does ...
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2 votes
1 answer
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European call option on constant volatility or drawn from a volatility distribution

Which is more expensive: A European call option on constant volatility of 30% or or drawn from a random distribution of mean 30%? The answer in A Practical Guide To Quantitative Finance Interviews, ...
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Seed Values guaranteed convergence of Implied Volatility Calculation

Looking for good seed values for Newton Raphson to guarantee convergence of implied volatility calculation for a few models, all of which are for equities that have divs. 1) Bjerksund-Stensland 2002; ...
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1 vote
2 answers
270 views

How do I prove that a certain price is price of European option in Black-Scholes framework

I want to show whether the following price at t is of a european option in Black-Scholes Framework. $$S_tlog_e (S_t^3) $$ Is it just trying to substitute the function (and partial derivates) in the ...
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is price of multiple option strategy linear under expectation? [closed]

I wonder if someone can confirm (or refute) that the expected payoff of several option (in a strategy such as a spread, condor, etc) behaves as "expection of a sum is sum of expectations". ...
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-4 votes
1 answer
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Single-period market with probability space [closed]

Let $C^E$, $P^E$, $C^A$, and $P^A$ denote prices of a European call option, a European put option, an American call option and an American put option, respectively. All of them with expiry time $T$ ...
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0 votes
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Issue in Understanding the Boundary Conditions for European Call Option in Implicit Finite Difference Method

I have a working Python code which prices European call option in Implicit Finite Difference setting. However, I am unable to understand the Boundary Conditions implemented on the coefficient matrix ...
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1 vote
0 answers
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Put-call parity under a regime-switching model

I need some help. I'm given $J$ different regimes, each one characterized by its own parameters $(r_i, \delta_i,\sigma_i,...)$ with $i\in \mathcal{J}= \{1,2,...,J\}$ ($r$ = risk-free interest rate, $...
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Reason to hedge a European call option

Assume I write a call option on one share of the stock that I have. After selling the option I have an obligation to sell one share of the stock at some future time. I already have the stock, why ...
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Why are there so many S&P 500 call options selling with strike @1000?

I am analysing option-implied RNDs and risk preferences for my masters thesis, so forgive me if I sound like a beginner in derivatives. I use WRDS to download my historic options data. I am looking at ...
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3 answers
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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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