The tag has no wiki summary.

learn more… | top users | synonyms

9
votes
2answers
376 views

When is it rational to exercise a bond option early?

Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
7
votes
2answers
130 views

American Call: when it's European?

It is a rather well-spread fact that in Black-Scholes (BS) model for a stock with no dividends that follows Geometric Brownian Motion (GBM), the price of American call coincides with that of its ...
6
votes
3answers
333 views

How to choose a risk-neutral measure when the market is incomplete?

I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model. Like most stochastic ...
6
votes
2answers
2k views

Implied Volatility from American options (binomial)

I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock). I believe it is ...
6
votes
1answer
265 views

Upper bound concerning Snell envelope

Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its ...
5
votes
7answers
10k views

Exercising an American call option early

I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it. If the option strike price is $E=\$20$ and it expires at $T=1yr$, if ...
5
votes
1answer
126 views

Intuition behind American Option pricing

The price of an American option is given by $$V_n = \max\left(G_n,\frac{pV_{n +1}H^d + qV_{n + 1}H^u}{1 + r}\right)$$ where p, q are the risk neutral probabilities. I have two questions: How can ...
5
votes
1answer
614 views

Modified bisection formula for deriving implied volatility for a dividend paying american option

I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield). On page 171 of Haug The ...
5
votes
1answer
2k views

Longstaff-Schwartz (Least Squares Monte Carlo) applied to American Options

I'm working on an implementation in R of Longstaff & Schwartz method from the this 2001 article. I've managed to build code that replicates their prices in table 1 (p. 127), but only for the ones ...
5
votes
0answers
117 views

Pricing an American call under the CGMY model

I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x $ for $i=0,1,...N$ and $\Delta ...
5
votes
0answers
46 views

Does price of american (put) option exhibit smooth pasting in time direction under B-S model?

Let us consider the BS model and let $f(s,t)$ denote the price of an American put option with $t$ to expiry, then it is known the solution of the optimal stopping (when it is risk neutral) related to ...
5
votes
0answers
142 views

American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t. $$ C_t = (\delta \sum_{j=n+1}^{M+1} ...
4
votes
1answer
244 views

Estimating early exercise boundary for American put

I am trying to estimate the early exercise boundary for an American put option. I can find the put value through the Longstaff-Schwartz LSM method. How do I obtain the early exercise boundary within ...
4
votes
2answers
177 views

Machine learning for non optimal behaviour

I was working on the pricing of complex bermudean swaption when I noticed that the exercise is often (very) subobptimal. It seems that the clients are more sensitive to past growth or drop in rates ...
4
votes
2answers
3k views

Value of American Call vs Value of European Call when using implicit finite differences

I calculated values for put options (european and american) using the implicit finite difference method and compared them to black/scholes values. The values for american put options are higher than ...
4
votes
1answer
450 views

What's the connection between implied vol curve of SPX and SPY?

I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 ...
4
votes
1answer
513 views

Black-Scholes American Put Option

Here is my question: This is a question about Black-Scholes model, but it may be applicable to more complicated models. Throughout the discussion, the strike price $K$, interest rate $r$ and ...
3
votes
2answers
318 views

Pricing an american style option on a bond future

what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue ...
3
votes
2answers
66 views

American put for negative interest rates

It is often explained, that the rule of thumb for exercising American options is to check when the benefit from the interest rate (sell the stock earlier, get the cash, put in the bank) is higher than ...
3
votes
1answer
135 views

Literature on Empirical Option Pricing

When I started combing through the literature I was astonished about how little the option pricing models are tested against market data and benchmarks are limited. The main barrier is of course ...
3
votes
1answer
63 views

Methodology for handling short american options in a back test

Given that an American option can be exercised at any time, how does one handle algorithmically shorting an American option in a back test? I am not sure what the best practice is to simulate the ...
3
votes
1answer
122 views

Why future (forward) volatility smile is important to path dependent option?

I was wondering why future volatility smile is important to path dependent option and American type option such as Bermudan swaption. It would be best if someone could provide a reference article as ...
3
votes
0answers
39 views

How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
3
votes
0answers
130 views

Constructing Volatility Smile from American Options

My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ...
3
votes
0answers
82 views

LSM American Option pricing with dividends

Under the Longstaff-Schwartz LSM method for an American call, how should I account for a continuous dividend paying stock? I assume that it'll needs to be accounted for when simulating the underlying ...
2
votes
1answer
117 views

How are option expiration dates decided?

I looked at the CBOE website and they say the expiration is the Saturday following the third Friday of each month. However, I look up an options chain for Google, for example, and I see three ...
2
votes
2answers
80 views

Hedging portfolio and extraction PDE of SV model with stochastic interest rate

How can I extraction this PDE \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + \frac{1}{2}P_{\sigma ...
2
votes
1answer
96 views

Boundary conditions of PDE from SV model with stochastic interest rate

The PDE for the American put option price $P(S,\sigma ,r,t)$ is \begin{align*} 0 =& P_t+P_SS(r-\delta)+P_\sigma a(\sigma)+P_r\alpha (r,t) \\ +& \frac{1}{2}P_{SS}S^2\sigma ^2 + ...
2
votes
1answer
71 views

How can one value a Bermuda option?

A Bermuda option allows early exercise at predefined dates, e.g. at maturity equal to $t_1$, $t_2$, $t_3$,...; hence , would its value be the sum of 3 discounted European options with 1-year ...
2
votes
1answer
63 views

Value of European Call equals Value of American Call, Question on Explanation/Proof

I am reading S. Shreve, Stochastic Calculus for Finance, Vol. I. There he proves that American Call Options have the same value as European Call Options. In the proof he uses that for a Call option ...
2
votes
0answers
115 views

negative transition probabilities in the heston model

I've been trying to implement a bivariate tree for pricing american options with the heston model in R using the paper of Beliaeva and Nawalkha ...
1
vote
4answers
69 views

analytic formula for the value of an American put option

It seems to be a foolish question but I can't take my mind off from , Is it true that there is no analytic formula for the value of an American put option on a non-dividend-paying stock (or a divident ...
1
vote
2answers
213 views

How to price long dated options most efficiently?

hi question is how to price a long dated option most computationally efficiently? With European, you use Black Shoals (yes assumption constant vol/rates...etc) but it's a simple algebraic formula. ...
1
vote
2answers
743 views

Relationship between European, American options volatility

Suppose, if the price of a European option (say a put) can be shown to be monotone in volatility (say for any maturity), does it follow that American options has to be monotone in volatility? ...
1
vote
2answers
5k views

Early execise of American Call on Non-Dividend paying stock.

Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
1
vote
1answer
67 views

Pricing American with floating strike

Consider a American floating strike put option with maturity $T$, written on a non-dividend paying stock $S_t$. The strike of this option at time $t\leq T$ is $Ke^{-r (T-t )}$, where $r$ is the ...
1
vote
2answers
93 views

Efficient numerical approaches for pricing American Options with multiple sources of noise

I am looking for efficient numerical approaches for pricing American options when two or more sources of noise are involved (the simplest case coming to mind would be the Heston Model) Eventhough I ...
1
vote
1answer
47 views

Hedging behind the decomposition of american put options

Now I'm reading a paper:"alternative characterizations of american put options" , the authors are Carr,Jarrow,Myneni http://www.math.nyu.edu/research/carrp/papers/pdf/amerput7.pdf After theorem 1 ...
1
vote
0answers
52 views

Price of an American call option [closed]

I'm working through revision questions at the moment and we are asked to compute the price of an American call option. Suppose that $dS_t = \sigma S_t dW^*_t, S_0 >0$ Let $0<U<T$ be fixed ...
1
vote
0answers
93 views

American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
0
votes
3answers
250 views

What is the effect of dividend yield being greater than the risk-free rate to American options pricing?

Even though dividends are discrete, literature often makes the assumption of continuous dividends (mostly in the case of indices but the individual stocks as well). The dividend yield denoted by q is ...
0
votes
0answers
126 views

Implied volatility from American options using python

I am currently trying to construct volatility surface from american option prices (using Cox-Ross-Rubinstein tree) in Python 2.7. Below you can find the code I came up with. Any corrections would be ...
0
votes
1answer
49 views

Are “American” option strategies traded OTC?

Is there such a thing as an American butterfly spread? For a European butterfly spread simply buying 1 put with strike price X+a, 1 put with strike price X-a and shorting 2 calls with strike price X, ...
0
votes
0answers
41 views

Complicated American style option contract with numerous non-standard features (simultanous exercise, additional premium, etc.)

I want to value the following contract for times $0<t<T$, i.e. determine $V(t,\cdot)$ where $\cdot$ refers to all other dependences (strike, spot, volatility, etc.). The contract is long and ...