# Tag Info

## Hot answers tagged european-options

Accepted

### Prove that the butterfly condition is always greater than zero

You generally can't simply subtract two inequalities as you did in your attempt. Here are two approaches to solve your problem: No-Arbitrage Argument Assume that the initial value of the Butterfly ...
• 6,084
Accepted

### Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option

Gamma and vega have the same general shape , peaking at ATM and tapering to the tails. But gamma concentrate as the option gets closer to expiry (when vega is small). For options a long way from ...
• 1,113

### Do basket options have a closed form valuation formula?

I'm not completely certain from your question, but I'm going to assume you have a basket of $n$ stocks with prices $S_0(t)$ to $S_n(t)$, and you want to price an option with payoff at $C(\tau)$ at ...
• 3,056

That's nice. Starting from $$C = e^{-r T}N_2 (F-K) + (N_1 - N_2) S$$ we can substitute $F= e^{r T}S$ (no dividend case) so we get $$C = e^{-r T}N_2(e^{r T} S-K) + (N_1 - N_2) S =$$ = N_1 S -e^{-r T}... • 11.6k 7 votes ### Option pricing and mean reversion From the SDE \begin{align*} \frac{dS_t}{S_t}= k(\theta-\ln S_t) dt + \sigma dW_t, \end{align*} where \{W_t,\, t\ge 0\} is a standard Brownian motion, we obtain that \begin{align*} d(e^{kt}\ln S_t) = ... • 21.2k 7 votes Accepted ### How do I prove that a certain price is price of European option in Black-Scholes framework Yes it is actually just substituting it into the Black Scholes PDE. If the PDE is satisfied, V(t,S(t)),t\ge 0 is a martingale and hence V(t,S(t)) = E_t (V(T,S(T)) so that V(t,S(t)) is the ... • 940 6 votes ### Dependency of an option price on time till expiry You've tagged this with 'black-scholes' but you don't have to make the assumptions of the Black-Scholes-Merton model to understand why the option price with time to expiry. Consider this example: ... • 8,581 6 votes Accepted ### Compute the price of a derivative If you plot the function f, you see that you have a bear spread. You can build such vertical spreads either with call or put options. For example consider a portfolio selling one put option with ... • 16.2k 6 votes Accepted ### Valuation of non-deliverable option Without loss of generality, for a European call option with payoff (S_T-K)^+ at expiry T, whether the option is settled in cash or rather the strike/asset are exchanged should in theory have no ... • 8,169 5 votes ### A simple question: Cost of delta hedging when a call option is sold You should go back to the derivation of the Black-Scholes equation (see this answer for example). The main point is that you can cancel the risk of the derivative over an infinitesimal time period dt... • 3,946 5 votes ### Can increase in volatility reduce the price of a deeply in-the-money European put? If you hold an option, you're always vega long, i.e. if volatility increases, your position increases as well - regardless of moneyness and the option type (put or call). Note firstly that by the ... • 16.2k 5 votes ### Compute the price of a derivative It would be much easier to start by writing the payoff using indicator functions. For example, \begin{align*} f(S_T) &= 3 \mathbb{I}_{S_T \le 30} + (33-S_T) \mathbb{I}_{30<S_T < 35} -2 \... • 21.2k 5 votes Accepted ### Can strike prices of options be negative? If the underlying asset cannot be negative, then an option on it with a negative strike would be meaningless. A call would always be in-the-money with no chance of being worthless, and a put would ... • 1,511 5 votes ### Proof European call price is always less than stock price. (proof verification) What you need to note is the following: \begin{align*} S_T - \max(S_T-K, \,0) &= S_T + \min(K-S_T, \,0)\\ &=\min(K, \, S_T) >0. \end{align*} • 21.2k 5 votes ### Why are there so many S&P 500 call options selling with strike @1000? I'm also currently working on analyzing option-implied RNDs. I'm no expert but a couple of comments: In addition to volume, you want to look at the open interest of the different strikes to conclude ... • 760 5 votes ### What is the intuition behind a positive theta for European long puts? It’s just the effect of interest. If you are long a deep ITM European put, it is worth the PV of K minus the stock price. But one day later the PV of K has grown a bit. That’s it. It’s the opposite ... • 17.5k 5 votes Accepted ### Why is this inequality strict for arbitrage argument for European call? It is because to show the existence of arbitrage, it suffices to show that there is no chance of losing money,and a positive chance of making money. Arbitrage does not imply you are certain to make ... • 17.5k 4 votes ### Prove that the butterfly condition is always greater than zero it's a model-free result. The pay-off is non-negative everywhere and positive somewhere. Since it's non-negative everywhere, if its price was negative there would be a clear arbitrage. We have to ... • 6,993 4 votes Accepted ### How to make the arbitrage if intrinsic value is greater than European call value how to construct the portfolio (St−K)+ or how to make this arbitrage If you have this scenario on your hands then you construct the portfolio by putting as much capital as you can into the trade. It'... • 4,368 4 votes ### How to make the arbitrage if intrinsic value is greater than European call value The intrinsic value of a call is the price of the underlying minus the strike (S0-K), so if you find a european call whose value is less that that you would: Sell (... • 1,511 4 votes ### Is there any useful links for option pricing (american + asian + european) using R Below is an example of how you could plot a "call" option value with RQuantLib: ... • 1,704 4 votes ### Valuation of Bermudan option as maximum of relevant European options You are wrong. Using the maximum of the prices of the European options is equivalent to choosing (and making that choice final) on t=0 the date t_i on which you will exercise. As such a choice ... • 5,702 4 votes ### A simple question: Cost of delta hedging when a call option is sold Based on the inputs from other users, this is another non-rigorous proof of why the cost of delta-hedging is equal to the option price. This approach might be useful for students who use John Hull for ... • 277 4 votes Accepted ### Why do we need to calibrate vega? It seems like he is assuming that the shorter term volatilities change more than the longer term ones and the relatively sensitivity is proportional to 1 / \sqrt{T}. Thus, this hedge is not against ... • 6,084 4 votes ### How to calculate implied correlation via observed market price (Margrabe option) We know that -1\le\rho_{imp}\le 1 so perhaps the simplest approach is to try the possible values \rho_{imp}=\{-1,-0.9,-0.8,\cdots,0.8,0.9,+1\}, to calculate resulting \sigma values, d± values, ... • 9,402 4 votes ### Compute the price of a derivative Here's another way to do it, that I think is useful if you don't recognize/have knowledge of specific option spreads/techniques. This might help you on exams or other problems, although recognizing ... • 666 4 votes Accepted ### Monte Carlo option pricing with R Your code looks fine and it is encouraging that both MC simulations yield similar results. Please look at this simplified code for the analytical part of the Monte Carlo simulation. As you know,S_T=...
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