computer science

Korn–Kreer–Lenssen model

Korn–Kreer–Lenssen model is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Korn–Kreer–Lenssen model rather than just read about it. In short: The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on these. It generalizes the binomial Cox-Ross-Rubinstein model in a natural way as the stock in a given time interval can either rise one unit up, fall one unit down or remain unchanged.

Key takeaways

Korn–Kreer–Lenssen model belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Korn–Kreer–Lenssen model to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Korn–Kreer–Lenssen model from memory before moving on to harder problems.

Reference excerpt

The Korn–Kreer–Lenssen model (KKL model) is a discrete trinomial model proposed in 1998 by Ralf Korn, Markus Kreer and Mark Lenssen to model illiquid securities and to value financial derivatives on these. It generalizes the binomial Cox-Ross-Rubinstein model in a natural way as the stock in a given time interval can either rise one unit up, fall one unit down or remain unchanged. In contrast to Black–Scholes or Cox-Ross-Rubinstein model the market consisting of stock and cash is not complete yet. To value and replicate a financial derivative an additional traded security related to the original security needs to be added. This might be a Low Exercise Price Option (or short LEPO). The mathematical proof of arbitrage free pricing is based on martingale representations for point processes pioneered in the 1980s and 1990 by Albert Shiryaev, Robert Liptser and Marc Yor. The dynamics is based on continuous time linear birth–death processes and analytic formulae for option prices and Greeks can be stated. Later work looks at market completion with general calls or puts. A comprehensive introduction may be found in the attached MSc-thesis. The model belongs to the class of trinomial models and the difference to the standard trinomial tree is the following: if Δ t {\displaystyle \Delta t} denotes the waiting time between two movements of the stock price then in the KKL-model Δ t {\displaystyle \Delta t} remains finite and exponentially distributed whereas in trinomial trees the time is discrete and the limit Δ t → 0 {\displaystyle \Delta t\rightarrow 0} is taken by numerical extrapolation afterwards.

See also Binomial options pricing model Trinomial tree Valuation of options Option: Model implementation

References

Literature Ralf Korn, Markus Kreer and Mark Lenssen: "Pricing of european options when the underlying stock price follows a linear birth–death process", Stochastic Models Vol. 14(3), 1998, pp. 647–662 Xiong Chen: "The Korn–Kreer–Lenssen Model as an alternative for option pricing", Willmott Magazine June 2004, pp. 74–80

Worked examples

Example 1 — a first encounter with Korn–Kreer–Lenssen model

Start with the simplest possible case. Write down what Korn–Kreer–Lenssen model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Korn–Kreer–Lenssen model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Korn–Kreer–Lenssen model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Korn–Kreer–Lenssen model

In research: Korn–Kreer–Lenssen model appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Korn–Kreer–Lenssen model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Korn–Kreer–Lenssen model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Financial models, Mathematical finance, Models of computation, so understanding it makes those chapters shorter.
In everyday life: Look for Korn–Kreer–Lenssen model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Korn–Kreer–Lenssen model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Korn–Kreer–Lenssen model means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Korn–Kreer–Lenssen model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Korn–Kreer–Lenssen model in simple terms?

Why does Korn–Kreer–Lenssen model matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Korn–Kreer–Lenssen model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Korn–Kreer–Lenssen model.