University of Isfahan Journal of Asset Management and Financing 2383-1189 14 2 2026 06 22 Pricing the Default Risk Factor in Short-Term Debt: A Compound Option Approach in the Iranian Capital Market Pricing the Default Risk Factor in Short-Term Debt: A Compound Option Approach in the Iranian Capital Market 109 134 29780 10.22108/amf.2025.145501.1993 FA Mahnaz Khorasani Ph.D. Candidate, Department of Industrial Management, Faculty of Economics, Management and Administrative Sciences, Semnan University, Semnan, Iran Gholamhossein Golarzi Associate Professor, Department of Business Management, Faculty of Economics, Management and Administrative Sciences, Semnan University, Semnan Iran. Seyed Kazem Ebrahimi Associate Professor, Department of Accounting, Faculty of Economics, Management and Administrative Sciences, Semnan University, Semnan, Iran 0000-0002-7227-6407 Journal Article 2025 06 01 This study introduces and integrates short-term debt default risk as a novel systematic factor into the capital asset pricing framework and evaluates its impact on the explanatory power of existing multi-factor models in the Iranian capital market. Employing the structural Geske model—a compound option pricing approach—we estimate the default probabilities of short-term debt for firms listed on the Tehran Stock Exchange and Iran Fara Bourse between 2004 and 2023. These probabilities, derived through numerical solutions of nonlinear equation systems, serve as the basis for constructing a default risk factor, which is then incorporated into standard multi-factor asset pricing models. Time-series regressions were performed on test portfolios sorted by short-term default probability, as well as on control portfolios constructed without this characteristic for robustness. The results demonstrate that the inclusion of the short-term default risk factor significantly enhances the explanatory power of asset pricing models across both portfolio types, underscoring its relevance as a priced risk factor in the Iran`s capital market. Keywords: Asset Pricing Factor Models, Compound Option, Short-Term Debt Default Risk, Stock Returns JEL Classification: C22, C51, G12, G33 Introduction Short-term debt default risk—the probability that a firm will fail to meet its immediate financial obligations—has garnered increasing scholarly interest, particularly in financial systems where firms exhibit high dependence on short-term borrowing and face persistent refinancing requirements (Corvino & Fusai, 2022; Li & Sun, 2023). This form of risk is acutely heightened during periods of liquidity stress, amplifying corporate financial fragility. A body of empirical research across both developed and emerging markets—including the U.S., China, Europe, and Australia—affirms that default risk is a significant determinant of equity pricing (Chen & Hill, 2013; Li & Sun, 2023; Yang & Hu, 2024). Nevertheless, conventional asset pricing models have predominantly neglected to incorporate short-term debt default risk as an explicit, standalone risk factor (Li & Lin, 2021). This oversight is particularly consequential in the context of the Iranian capital market, where short-term instruments comprise a substantial share of corporate financing structures. To address this gap, this study investigates the hitherto unexplored role of short-term debt default risk in explaining stock returns within this market. Employing the structural Geske (1977) model—an extension of the Merton (1974) framework based on compound option pricing—we estimate a novel risk factor proxying for the probability of short-term default. This factor is subsequently integrated into three established asset pricing models: the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965), the q-factor model by Hou et al. (2015), and the six-factor model of Fama and French (2018). The central aim of this study is to determine whether the inclusion of this default risk factor significantly enhances the explanatory power of these benchmark models. By constructing a theoretically grounded and empirically tested risk factor, this study contributes to the asset pricing literature and offers insights of practical relevance to both investors and policymakers operating in the Iran`s capital market. Materials and Methods This study employs an applied, ex post facto research design to examine the effect of short-term debt default risk on the explanatory power of asset pricing models. The population consists of all firms listed on the Tehran Stock Exchange (TSE) and Iran Fara Bourse (IFB) from 2004 to 2023. The sample was filtered according to criteria established in seminal asset pricing studies, including Fama and French (1993, 2015, 2018), Ball, Gerakos, Linnainmaa, and Nikolaev (2016), and Li and Lin (2021). Exclusions encompassed firms in the over-the-counter (OTC) base market, financial institutions, entities with negative book value, those experiencing extended trading halts, and firms with insufficient data availability. The final sample comprised 335 firms. Data were collected from the Tehran Securities Exchange Technology Management Company and Rahavard Novin software. Short-term debt default probabilities were estimated using the Geske (1977) model—a compound option extension of the Merton (1974) framework—by solving systems of nonlinear equations with multivariate normal distribution functions in MATLAB. Asset pricing model estimation and time-series regression analyses were conducted in Python. Factors constructed included the market risk premium (MRP), size (SMB), value (HML), profitability (RMW), investment (CMA), momentum (MOM), and the novel short-term default risk factor (STD). These factors were formed using the Fama and French (1993, 2015) independent 3×2 sorting methodology. Model performance was evaluated using time-series regressions on test portfolios sorted by short-term default probability, with robustness checks performed on control portfolios not sorted by this characteristic. Statistical significance was assessed using intercept (alpha) estimates and the Gibbons, Ross, and Shanken (1989) (GRS) test, consistent with the Fama and French empirical tradition. Findings The descriptive analysis indicates that the short-term debt default risk factor (PMD) carries a positive and statistically significant average return of 0.47%, consistent with the existence of a positive risk premium in the market. PMD demonstrates a positive correlation with the market factor and negative correlations with both profitability and investment factors. Time-series regression results reveal that the inclusion of the PMD factor significantly enhances the explanatory power of all asset pricing models examined. Specifically, augmenting the CAPM with PMD leads to a notable reduction in both the GRS statistic and the average absolute value of intercepts (A|αᵢ|), indicating a superior model fit. This improvement is further corroborated by declines in the metrics A|αᵢ| / A|r̄ᵢ| and A|αᵢ²| / A|r̄ᵢ²|, which signify a reduction in the proportion of cross-sectional return dispersion and variance that remains unexplained by the model. Parallel enhancements in model performance were observed when PMD was integrated into both the q-factor and the Fama-French six-factor (FF6) models. Across all augmented specifications (CAPM+PMD, q+PMD, FF6+PMD), the models consistently outperformed their original counterparts. This superior performance was robust across both double-sorted (5×5) and triple-sorted (2×4×4) portfolio formations. Crucially, robustness checks confirmed that these improvements are not an artifact of the sorting variable; even in test portfolios constructed without regard to default probability, the inclusion of PMD resulted in lower GRS statistics and diminished pricing errors. Discussion and Conclusion In conclusion, this study establishes that short-term debt default risk, a pivotal element of credit risk, is a significant determinant of stock returns, especially in markets characterized by a high reliance on short-term financing. While traditionally overlooked by mainstream asset pricing models, this omission potentially leads to biased estimates of expected returns. To address this gap, we developed a novel risk factor (PMD) grounded in the Geske (1977) compound option model and integrated it into three established asset pricing frameworks: the CAPM, the q-factor model, and the Fama-French six-factor model. Empirical analysis, conducted via time-series regressions on a sample of 335 firms from the Tehran Stock Exchange and Iran Fara Bourse (2004–2023), demonstrated that the inclusion of the PMD factor consistently and significantly enhanced the explanatory power of all models. This improvement was robust across test portfolios sorted by size, book-to-market, investment, profitability, and default probability, and was quantified by lower GRS statistics, reduced average absolute alphas, and decreased pricing error ratios. Crucially, the factor's efficacy extended to portfolios constructed without a default-risk characteristic, underscoring its role as a pervasive, non-diversifiable systematic risk factor within the Iranian capital market, rather than a mere idiosyncratic variable. This study introduces and integrates short-term debt default risk as a novel systematic factor into the capital asset pricing framework and evaluates its impact on the explanatory power of existing multi-factor models in the Iranian capital market. Employing the structural Geske model—a compound option pricing approach—we estimate the default probabilities of short-term debt for firms listed on the Tehran Stock Exchange and Iran Fara Bourse between 2004 and 2023. These probabilities, derived through numerical solutions of nonlinear equation systems, serve as the basis for constructing a default risk factor, which is then incorporated into standard multi-factor asset pricing models. Time-series regressions were performed on test portfolios sorted by short-term default probability, as well as on control portfolios constructed without this characteristic for robustness. The results demonstrate that the inclusion of the short-term default risk factor significantly enhances the explanatory power of asset pricing models across both portfolio types, underscoring its relevance as a priced risk factor in the Iran`s capital market. Keywords: Asset Pricing Factor Models, Compound Option, Short-Term Debt Default Risk, Stock Returns JEL Classification: C22, C51, G12, G33 Introduction Short-term debt default risk—the probability that a firm will fail to meet its immediate financial obligations—has garnered increasing scholarly interest, particularly in financial systems where firms exhibit high dependence on short-term borrowing and face persistent refinancing requirements (Corvino & Fusai, 2022; Li & Sun, 2023). This form of risk is acutely heightened during periods of liquidity stress, amplifying corporate financial fragility. A body of empirical research across both developed and emerging markets—including the U.S., China, Europe, and Australia—affirms that default risk is a significant determinant of equity pricing (Chen & Hill, 2013; Li & Sun, 2023; Yang & Hu, 2024). Nevertheless, conventional asset pricing models have predominantly neglected to incorporate short-term debt default risk as an explicit, standalone risk factor (Li & Lin, 2021). This oversight is particularly consequential in the context of the Iranian capital market, where short-term instruments comprise a substantial share of corporate financing structures. To address this gap, this study investigates the hitherto unexplored role of short-term debt default risk in explaining stock returns within this market. Employing the structural Geske (1977) model—an extension of the Merton (1974) framework based on compound option pricing—we estimate a novel risk factor proxying for the probability of short-term default. This factor is subsequently integrated into three established asset pricing models: the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner (1965), the q-factor model by Hou et al. (2015), and the six-factor model of Fama and French (2018). The central aim of this study is to determine whether the inclusion of this default risk factor significantly enhances the explanatory power of these benchmark models. By constructing a theoretically grounded and empirically tested risk factor, this study contributes to the asset pricing literature and offers insights of practical relevance to both investors and policymakers operating in the Iran`s capital market. Materials and Methods This study employs an applied, ex post facto research design to examine the effect of short-term debt default risk on the explanatory power of asset pricing models. The population consists of all firms listed on the Tehran Stock Exchange (TSE) and Iran Fara Bourse (IFB) from 2004 to 2023. The sample was filtered according to criteria established in seminal asset pricing studies, including Fama and French (1993, 2015, 2018), Ball, Gerakos, Linnainmaa, and Nikolaev (2016), and Li and Lin (2021). Exclusions encompassed firms in the over-the-counter (OTC) base market, financial institutions, entities with negative book value, those experiencing extended trading halts, and firms with insufficient data availability. The final sample comprised 335 firms. Data were collected from the Tehran Securities Exchange Technology Management Company and Rahavard Novin software. Short-term debt default probabilities were estimated using the Geske (1977) model—a compound option extension of the Merton (1974) framework—by solving systems of nonlinear equations with multivariate normal distribution functions in MATLAB. Asset pricing model estimation and time-series regression analyses were conducted in Python. Factors constructed included the market risk premium (MRP), size (SMB), value (HML), profitability (RMW), investment (CMA), momentum (MOM), and the novel short-term default risk factor (STD). These factors were formed using the Fama and French (1993, 2015) independent 3×2 sorting methodology. Model performance was evaluated using time-series regressions on test portfolios sorted by short-term default probability, with robustness checks performed on control portfolios not sorted by this characteristic. Statistical significance was assessed using intercept (alpha) estimates and the Gibbons, Ross, and Shanken (1989) (GRS) test, consistent with the Fama and French empirical tradition. Findings The descriptive analysis indicates that the short-term debt default risk factor (PMD) carries a positive and statistically significant average return of 0.47%, consistent with the existence of a positive risk premium in the market. PMD demonstrates a positive correlation with the market factor and negative correlations with both profitability and investment factors. Time-series regression results reveal that the inclusion of the PMD factor significantly enhances the explanatory power of all asset pricing models examined. Specifically, augmenting the CAPM with PMD leads to a notable reduction in both the GRS statistic and the average absolute value of intercepts (A|αᵢ|), indicating a superior model fit. This improvement is further corroborated by declines in the metrics A|αᵢ| / A|r̄ᵢ| and A|αᵢ²| / A|r̄ᵢ²|, which signify a reduction in the proportion of cross-sectional return dispersion and variance that remains unexplained by the model. Parallel enhancements in model performance were observed when PMD was integrated into both the q-factor and the Fama-French six-factor (FF6) models. Across all augmented specifications (CAPM+PMD, q+PMD, FF6+PMD), the models consistently outperformed their original counterparts. This superior performance was robust across both double-sorted (5×5) and triple-sorted (2×4×4) portfolio formations. Crucially, robustness checks confirmed that these improvements are not an artifact of the sorting variable; even in test portfolios constructed without regard to default probability, the inclusion of PMD resulted in lower GRS statistics and diminished pricing errors. Discussion and Conclusion In conclusion, this study establishes that short-term debt default risk, a pivotal element of credit risk, is a significant determinant of stock returns, especially in markets characterized by a high reliance on short-term financing. While traditionally overlooked by mainstream asset pricing models, this omission potentially leads to biased estimates of expected returns. To address this gap, we developed a novel risk factor (PMD) grounded in the Geske (1977) compound option model and integrated it into three established asset pricing frameworks: the CAPM, the q-factor model, and the Fama-French six-factor model. Empirical analysis, conducted via time-series regressions on a sample of 335 firms from the Tehran Stock Exchange and Iran Fara Bourse (2004–2023), demonstrated that the inclusion of the PMD factor consistently and significantly enhanced the explanatory power of all models. This improvement was robust across test portfolios sorted by size, book-to-market, investment, profitability, and default probability, and was quantified by lower GRS statistics, reduced average absolute alphas, and decreased pricing error ratios. Crucially, the factor's efficacy extended to portfolios constructed without a default-risk characteristic, underscoring its role as a pervasive, non-diversifiable systematic risk factor within the Iranian capital market, rather than a mere idiosyncratic variable.

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