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# Questions tagged [longstaff-schwartz]

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4 votes
2 answers
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### Foresight bias in least square monte carlo

Foresight bias means we tend to over estimate the American option value. This we observe in other areas of statistics - e.g. in sample test almost always gives better prediction than out of sample ...
• 1,023
3 votes
0 answers
138 views

### Continuation value in Longstaff-Schwartz: Why the expected value?

In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by: \begin{align} F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
• 581
2 votes
0 answers
2k views

### Longstaff-Schwartz, special american option simulation using Python (numpy package)

I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$. Respectively, if exercised at ...
• 273
1 vote
1 answer
213 views

### L2 Assumptions of the Longstaff Schwartz method

In page 121 of the original LS Paper they use the fact that the space of functions they are dealing with (payoffs of American options), belong to the $\mathcal L^2$ space. They use this assumption ...
• 761
1 vote
1 answer
956 views

### Longstaff Schwartz algorithm

I am new in finance, I have implemented the Longstaff Schwartz algorithm for pricing american otion - one asset (dimension = 1). My questions : Does this algorithm still efficient for a high ...
1 vote
0 answers
165 views

### Longstaff-Schwarz LS Monte Carlo - which approach is correct? [closed]

I'm trying to understand Least-Square Monte Carlo approach for pricing american options. I'm familiar with Tsitsiklis and van Roy (2001) approach where we are going backwards with: $V_T = h(S_T)$, ...
• 11
1 vote
1 answer
599 views

### Least Square Monte Carlo Longstaff-Schwartz method implementation problem

While trying to implement the Least Square Monte Carlo (LSMC) method by Longstaff-Schwartz I came across an error I am not quite sure how to fix. The method uses a regression method (be it Multiple ...
• 23
1 vote
0 answers
179 views

### Longstaff and Schwartz example in their paper

I was looking at the well known Longstaff and Schwartz paper "Valuing American Options by Simulation: A Simple Least-Squares Approach". There are a couple of examples where they applied the ...
• 741
1 vote
0 answers
195 views

### Longstaff Schwartz method (LSM): how to increase accuracy?

In the LSM method, I am currently (as they do in the paper) using weighted Laguerre polynomials as basis functions, about 3-5 of them. If I wish to increase the accuracy of my model, what should I do?...
• 11
0 votes
0 answers
148 views

### Longstaff & Schwartz algorithm - Python: American option cheaper than European option

I have implemented the Longstaff & Schwartz algorithm for pricing American Option in Python, but I ran into an issue while doing some experiments: sometimes, for the same option, I get a higher ...
• 101
0 votes
0 answers
126 views

### Suboptimality bias in least squares Monte Carlo for American options

In Monte Carlo pricing of American options we form two estimators: A high estimator that is biased upward because of "look-ahead" bias (i.e., at any given time we uses future information to ...
• 581
0 votes
1 answer
158 views

### Longstaff-Schwartz for any optimal stopping

Let's say I have the stock of General Motors and I assume some fancy model for the price of this stock and I have to sell it within a month. Can I use Longstaff-Schwartz algorithm to determine the ...
• 179
0 votes
0 answers
33 views

### Longstaff Schwartz with future conditional coupons

I've implemented the L-S algorithm for a simple put option. I want to value a more complex derivative which has future conditional coupons which only occur if the option is in the money. How would I ...
• 387