# Questions tagged [option-pricing]

Questions about models for the valuation of option contracts.

1,639 questions
Filter by
Sorted by
Tagged with
36 views

### Which is more Appropriate way to calculate Leverage with Options Contracts? [closed]

the connecting of words and bold colors was because of something here in the posting feature, it would not let me take it away when originally posted. i have re-copied and tried correct those errors. ...
24 views

### Some questions about the pricing and the construction of Fixed Coupon Notes (FCN) [closed]

I'm currently studying Fixed Coupon Notes (FCN) out of my own curiosity. I've already read some articles and watched a video about it. One of the articles about FCN: https://cegafi.medium.com/...
33 views

### Monte carlo pricing on zero coupon bon under the Vasicek model [closed]

I would like to price an European call on zero coupon bond under the Vasicek model. I am planning to follow the Excercise 33 (hereby) from Lamberton Lapeyre (Introduction au calcul stochastique ...
46 views

### Stopping times, question on exercise

I'm completing exercises from Steve Shreve - Stochastic Calculus for Finance I and I'm stuck on one subtask for which I can't find missing element for 11 stopping ...
97 views

### How to determine break-even price on a delta hedge?

Suppose there is a portfolio of short $x$ shares and long 1 call option. This call option has a strike and premium. If the stock moves up, you loss money on the short position but gain on the option ...
109 views

### Very close local volatility and implied volatility using Dupire's equation

I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
• 41
225 views

### Black and scholes option pricing

I have to solve the following problem in the Black and scholes model: find the price at anty $t\in[0,T)$ for an option whose payoff at the maturity is: 0 \ \ \ \text{if} \ S_T<K_1\\...
• 123
56 views

### In the derivation of the Black-Scholes PDE, using delta hedging, how is this linked to the risk neutral valuation? [closed]

I was reading this paper: http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf I don't understand the paragraph here: "The most interesting feature of the Black-Scholes PDE (8) is that ...
1 vote
56 views

### Why should delta-neutral backspread always result in credit?

Natenberg mentions in chapter titled "Volatility Spreads" : under the assumptions of a traditional theoretical pricing model, a delta-neutral ratio spread where more options are purchased ...
• 175
84 views

### Any innovations in mathematical processes behind option pricing models?

I am working on my thesis about option pricing models beyond classical Black-Scholes Model by looking for some recent innovations on mathematical processes behind the pricing structures. By that I ...
• 21
1 vote
138 views

• 110
1 vote
18 views

### Find the lower bound of a contingent claim in incomplete market

I'm trying to justify the lower bound for the price of a contingent claim (a European one) which is not marketable in an arbitrage free market. I would like to have your advice on my way to do it: ...
• 45
1 vote
51 views

### 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 ...
• 45
31 views

### Confusion about "cost" in option pricing paper by Cox-Ross-Rubinstein paper

I am trying to understand the paper "Option Pricing: A Simplified Approach" by Cox-Ross-Rubinstein (available online here). To my frustration, I already don't understand the paper starting ...
109 views

### European option with payoff $X_T^2$ [closed]

I have been ask to price a European option with payoff $H(X_T,T) = X_T^2$ using the equivalent martingale measure (EMM). For this I used the process: dX_t = r X_t dt + \sigma X_t d\...
1 vote
113 views

### Use of markov process in option pricing

In several books on asset pricing and more particularly when it concerns option pricing, I see the use of Markov process, they argue the computation is made easier with such process. Is this ...
• 45
52 views

### Option pricing in incomplete CRR model

I'm studying the way option can be priced in an incomplete market and I have found an example talking about the Cox-Ross-Rubinstein model with three path possible instead of 2, making the model ...
328 views

### ATM Implied Volatility and Expected Variance

This answer claims that $$\sigma^2_{ATM}\approx E^Q\left(\frac{1}{T}\int_0^T\sigma^2_t dt\right)$$ ie implied ATM vol = risk-neutral expectation of integrated variance. Is there some proof available? ...
• 686
28 views

### When is the gamma of an iron butterfly spread positive? (Assuming stock price at t=0 is equal to the highest strike price)

I know the Gamma of a butterfly using calls is $$\Gamma_{butterfly} = \Gamma_{C_{K_3}}-2\Gamma_{C_{K_3}}+\Gamma_{C_{K_3}}$$ Where K3-K2 are the same as K2-K1 and S=K1, But under what condition is the ...
116 views

### Payoff of a Butterfly spread under risk neutral measure is always positive for any t<T

In a situation where $$K_3-K_2=K_2-K_1=h>0$$ and $$K_1\le S_t\le K_3$$ where $$S_T=S_t.e^{[(r-\sigma^2/2)(T-t)+\sigma(W_T-W_t)]}$$ (i.e. Stock process follows GBM under the risk neutral measure). I ...
27 views

### How to compute the price range for an American call and put option?

A non dividend paying stock has the following details for its European option: Time to expiry – 1 year, Risk free interest (Continuous)- 5%, Exercise price = 42, Current Stock Price = 40, Call option=...
1 vote
60 views

### What is the optimal time for exercising American call and put option?

A 9 month American option (underlying) is known to pay dividend of USD 1 and USD 0.75 at the end of the ...
• 11
103 views

### implied vol smile relative to atm vols

Am I correct in saying that most stochastic vol models are meant to behave in a way that as atm vol goes up the smile comes down and risk reversals become "less stretched?" - by that i mean ...
• 11