The Partial LeastSquares Method Based Stock Index Option Pricing

1
The Partial Least-Squares Method Based Stock
Index Option Pricing
PLS09, Beihang

• Jingchao Zhang, Liyan Han
• School of Economics Management,
• Beihang University

2
1. Introduction

• Langstaff and Schwartz began to use the
  statistical methods in pricing of derivative
  securities in 2001. It combines Ordinary
  Least-Squares (OLS) regression method with
  simulation to value the American options.
• Lars Stentoft (2003) gives the proof for
  convergence of OLS, and points out the OLS method
  often underestimates the value of options.
• Zheng and Han (2004) present the Partial Least -
  Squares (PLS) based American option pricing and
  then Han, Mou and Wang (2006) put forward the
  Partial Least - Squares (PLS) method to
  convertible bond pricing.
• However, up to now the PLS based method for
  pricing stock index option is still absent.

3
2.The Model Frame

• European stock index option pricing model based
  on GARCH

• PLS pricing model of European stock index option

4
PLS pricing model of European stock index option

• -The approximate price of European call option
  drawn from GARCH model
• An indicator of Korean macroeconomic factor, such
  as inflation rate, GDP, exchange rate
• -The trading volume of KOSPI200 index component
  stocks
• - Sentimental indicators of Korean investors
• - Residual series.

5
3. Application to KOSPI200 Index Option

• The paper examines KOSPI200 index of KOREA. The
  sample period is consistent with the time span of
  KR4201C61859 (a kospi200 index option contract)
  from 2008-4-2 to 2008-6-12. The logarithmic
  return rate is calculated
• the closing price of KOSPI200 index at day t.

6
GARCH (1, 1) model is built
ARCH effect (volatility clustering) exists
,
7
The real price and model estimate comparison o f
KR4201C61859
8
PLS pricing modelling

• For PLS pricing modelling, 11 original
  independent variables are considered, i.e.
• call-estimate,
• KOSPI200 index trading volume/daily return,
  Korean composite index open price/high price/low
  price/closed price/trading volume,
• CRB spot index, CRB futures index, SP Asian 50
  index.
• By applying variance inflation factor (VIF) test,
  it shows the existence of heavy multicollinearity.

9
Sentimental Indicators

• Considering the impact of investors emotion on
  to the market index
• trading volume of KOSPI200,
• Turnover and trading volume of Korean composite
• Control for other independent variables the
  macro factor of Korea and the international
  market.

10
Output 1- the extraction effect test
11
Output 2-the explaining degree of variation by
PLS factors
12
Output 3Model Effect Weights
13
Output 4 Parameter Estimates for Centered and
Scaled Data
14
Output 5 The ranking list of VIP(Variable
Importance for Projection)
15
Conclusion

• 1.Combined GAGCH, PLS pricing method can take the
  macroeconomic factors and the investors'
  emotional indicators into account.
• Ranking of Variable Importance for Projection,
  for understanding the explanatory factors
• 2. KOSPI200 stock index option pricing